Okay y'all want full targ restoration au? Imagine a story with Rhaenys lives and raised by the Sand Snakes AND instead of Aegon living/Jon joining them give me a bastard Targaryen from either Aerys or Rhaegar combine it with Gendry's botched storyline of being a nobody raised to the throne...
Imagine the idea of this child (Let's call him Jaehaeron, after Jaehaerys I and Daeron II who are considered to be some of the best Targaryen kings). Jaehaeron, grew up a street rat (maybe we'll employ some of the Young Griff storyline and have him be a member of the Golden Company or have him be a sell sword with Daario) and knows the struggle of being lower class and fighting for a way to make something of himself. He's never had a family, anyone he's ever cared about he's lost, either to disease infighting, to the law etc. He's learned that he's just one of those people who doesn't get to be in a family.
Imagine him not knowing who he is, never known family and never wanting any, but he meets Daenerys. He joins her because he believes in her and her cause. He knows what it's like to fight for yourself but he wants to learn how to fight for those who can't do it themselves, and she seems like the right person to learn from. Daenerys knows the minute she sees him. Maybe she dreamt it, maybe she could see the ghost of her brother's in him, maybe blood just calls to blood. In any case, of course she hesitates at first to let him know. She gathers evidence from spies around the world, she studies his intentions/ his mannerisms/ his very heart to make sure that he's not like Viserys. And he's not, he's the first sign of home she's had in a long time. And she becomes his first taste of it, essentially granting him saftey to love people and not get killed over it.
Imagine Rhaenys training with the Snakes, surrounded by home and family, but still feeling like something is missing. Imagine her Uncle Oberyn bringing her news of Daenerys in Meereen. At first she's guilty for wanting to know her but Oberyn reassures her that no one can have too much family, in fact Daenerys across the sea might have too little. So she sets off, with the assurance that the full weight of Dorne is behind her. Imagine her meeting Daenerys, matching title for title and after the following silence grows to be too much Daenerys launches down from her seat and Rhaenys just knows that she's gained another sister. After hearing Jaehaeron's story she just gathers him up in her arms and bawls. While he can't replace Aegon, the hole in her chest labeled brother does shrink a little.
They work flawlessly together. Jaehaeron walks Rhaenys through life in Essos, maybe sprinkles in a little bit of personal stories. Dany and Rhae pour over the Targaryen history and tentatively start making plans for Valyria. Jay pretends to be not paying attention (he is) and he and Dany agree on most things and he actually sits in on a lot of her meetings with her citizens. They all have moments of impulsivity tempered with control, but generally Jaehaeron tends to be the patient one, he tends to wait for all the information to make a final decision. Daenerys has her ideals and her determination to make it happen. Rhaenys is very action oriented but also is aware that forgiveness can sometimes go a longer way than retribution.
He and Rhae both teach Daenerys how to fight. She comes out fighting best with an Arakh, which means after they teach the basics they bring in one of Daenerys' remaining Dothraki to teach her while they learn from Grey Worm (Missandei being taught as well) but generally the stick with the tools of their trades.
Daenerys introduces them to Viserion and Rhaegal and tells them of Drogon. As they grow closer to each other, they do so towards the dragons as well. You'd think Rhaenys would be drawn to Rhaegal but Rhaenys barely remembers her father so it's actually Viserion who she bonds with. In the right light his scales remind her of the sands of Dorne, his fire of the light that filtered through the tent she shared with the snakes, his eyes of each piece of gold she earned from their battles and conquests, and while she never knew Viserys she's not gonna let something like a bad namesake keep her from her dragon. Jaehaeron just thinks that Rhaegal exists to hate him. He shows no sign of interest towards Jay, so much so that it almost gives him a complex about not being a "true" Targaryen. But Jay is persistent. He's there whenever he can be, he's always the one to bring Rhaegal his meals, eventually he's able to get close enough to stroke the neck of Rhaegal and when they look into each other's eyes Jaehaeron realizes that it's not hatred or indifference, it's loneliness that's keeping Rhaegal from bonding with him. From then on Jay is in the line up the pyramid every day, to ask Dany to release the dragons from their cells.
Imagine if when Dany leaves on Drogon Tyrion does not start running things, Jay and Rhaenys do. Rhae judging from her experience and compassion, Jaehaeron from his knowledge on the ground and instincts. They take Tyrion's advice into account but also Missandei's, Grey Worm's, even Oberyn's opinions. Imagine Rhaenys truly getting to know the people, and slowly but surely she starts to fall in love with this land. Imagine Jay training the Meereeneans(?) Because the need to and because he doesn't want to see a single one of his citizens helpless. They follow in Dany's footsteps, ruling as she would, so when the slavers siege (because of course they would) the Targ's are ready for them. When Daenerys returns with the Dothraki she's met with her sister at the head of the Sand Snakes and the soldiers of Dorne. She sees her brother riding with the Second Sons and the Golden Company (who are now convinced honor is as good as gold). The battle for Meereen was over before it began, especially after the dragons join the fray. As soon as it's over Jaehaeron and Rhaenys are ecstatic (and also demand Dany teaches them how to ride).
Imagine if it's Oberyn who brings Olenna to Dany and her cause, and Yara knows Jay from years back so she's even more confident for her cause when she sees him at Daenerys' side. During her time away they managed to comission armor for the dragons and their riders. When Daenerys sets sail for Westeros her siblings are by her side, her dragons are safe above them, her best friends are at her back, and she has some of the wisest minds advising her (including/excluding Tyrion depending on how you feel about him). They have the Dothraki, the Unsullied, a decent amount of Ironborn, the Second Sons(with or without Daario depending on yada yada....), the Golden Company, and the whole Dornish army. They stayed long enough for the new Meereen Guard to have been sufficiently and leaders put in place. The citizen's hearts are behind their Targaryens and they know if they ever even fear trouble they will fly back to assure them.
Imagine that they do take King's Landing first. The dornish get the majority of the lower town evacuated before the gold cloaks even notice. The dragons decimate the scorpions early on, with only glancing blows thanks to the armor. Even the wildfire Cersei throws out as a last resort doesn't stop them and as the trio makes their way to the throne room they have to walk past the what little is left of Cersei's forces. They decide to pardon every soldier who bends the knee, the rest are set to work rebuilding the damage of the siege. Cersei is sentenced to execution, via dragonfire where the Sept of Baelor once stood.
Imagine that the Iron Throne does melt, but only enough to shape into a bench. Just like in Meereen, however this one is long enough to seat three. No arguments, no hesitation, the Targaryens work better as a family anyway.
They rule as one. They leave a small council in charge of King's Landing and set off to the rest of Westeros. They do meet some resistance but no one is strong enough to stand against them, and honestly after meeting them and hearing their vision no one even wants to. Then there's the north.
Depending on how anti stark you are you can visualize the war for the dawn however you like. But imagine them hearing through Jon's story, taking a stealth mission to observe the white walkers themselves. Imagine that in addition to granting them access to Dragonstone they also command soldiers from each kingdom. (Jon is... commanding troops? Attempting to make an alliance that doesn't have him bending the knee) Imagine a fleet of red Priestesses, giving their fire to each soldier (not just the dothraki cause why not??), Jorah fighting with Missandei and Grey Worm, and hiding Bran at the starks head table (which reminds us of Ned and how long it's been for all of them). Imagine not housing the innocents in the crypt (cause they have common sense) and actually send them to the godswood to be protected by some of their own soldiers but also Jay overhead on Rhaegal. Imagine Rhaenys on the front lines with Viserion lighting her way (no walker proof storyline=no Viserion death win-win). Imagine Danerys cutting the wights of from behind, and when spotting the night king she goes to meet him. (However you view the show end to the NK/the prince who was promised prophecy this is gonna Dany, sorry).
Imagine Jaehaeron fighting like hell for Winterfells innocents, dancing through the fire almost as though he's a part of it. Nothing seems to touch him. Imagine Rhaenys cutting through wights like paper, grinning from ear to ear cause she's riding on the battle high and the strength of the Sand Snake around her. Imagine that when Drogon's fire doesn't work, the Night King throws a sword into Dany's child's chest. She pulls it out of his chest plate(again thank you armor) and Drogon lights it ablaze. She meets the monster for blow. Seeing her in danger both Jaehaeron and Rhaenys make their way to her. Imagine the Night King dealing her a viscous blow but getting knocked down by a spear from Rhae and kept distracted by Jay. They give Dany enough time to stab the so called king in the back (mirroring when her father was lost and their kingdom was officially lost to them; all these years later her family is remade and the kingdom is theirs again). As Jon sees them from the remains of the wights, let's pretend no r+l=j or at least he doesn't know and if he found out there's no way he gets enough support to take the throne from them or feel the need to. He decides to bend the knee, only to find that the Targaryens don't really plan on keeping the kingdoms together, as they were anyway.
Being rulers does have its share of problems, especially as they dissolve the country into something more democratic but they make it work. One of them is always in Kings Landing, even with Rhaenys' frequent trips to Dorne and Meereen, Jaehaeron's explorations of Essos and his quest to rebuild Valyria, and Daenerys' continues mission to make every land truly free. They always make time for their people and each other.
And so while Daenerys is the Mother of Dragons she is also the Hero of the People, Rhaenys is the Fierce Queen from Dorne, and Jay is declared Jaehaeron the Fortunate and he cannot find reason to disagree. They each have their titles, their armies, their stories. But they also have each other. After all, the dragon has three heads.