Share three dragons who definitely can't make each other better, but CAN make each other worse.
That's 100% the Exorcism Trio. Absinthe, Petrichor, and The Gentleman are a trio made up of a priest, a priestess, and a swindling, flashy 'monster hunter' of an exorcist. They all perform the same duty, gathering and purifying the lingering magic of dead dragons that's formed into spirits and haunting activities, and have all arrived in Vaudemire Way at the same time, completely divorced of one another.
While Petri and Sin get along rather well, Gentleman is kind of an antagonistic douche, he and Fleck make their money misleading others into paying hand-over-fist for incidents that aren't exactly real- which means the very real hauntings around Vaudemire Way that the other two have arrived to investigate are a little out of his wheelhouse- but his ego won't let him admit that, especially not to Absinthe, as the young priest with his legitimate talents is quickly determined to be a 'threat' in Gentleman's eyes.
Petrichor does her best to keep the peace- they're here to help people, after all- surely the three of them can work together- though perhaps it's her lingering fondness for The Gentleman- he's a friend from childhood, after all, and the one to which she owes more than she'll ever admit to anyone but Gentleman himself. They've been settled in Vaudemire for a while, the three of them inhabiting the ramshackle Mirrors Apartments and Bar and doing their best to get to the bottom of the strange happenings around town separately.
They could work together, of course- but bickering is far more fun.
Share two dragons that hate-watch movies together.
They're like if Mystery Science Theater was allowed to drop the F bomb uncensored. Dethrone and Sow have no idea what effort goes into making films or acting but they know when they think something is stupid, and they tell you. to your face. loudly.
Share a dragon that should be in prison but currently isn't.
Honestly there's so many that fit this description but he was the first one to come to mind so it's absolutely Mal of the Diamond Riot. The leader of a crew of cybernetic tomb plundering, cattle-rustling, ne'er do wells, He's been blown up more times than he can count, and should have probably been to prison 5 times as many as those. He makes his living robbing tombs and stealing from others, and has been a scourge on Sornieth for ages alongside his friends and companions. The problem is he's certainly been arrested several times- he just keeps getting out.
Now though, in the depths of Dragonhome, in a lost city discovered in blind greed and at the risk of getting the only people who can kind of stand him killed by a massive, lumbering emperor, he probably wishes he'd served that last sentence instead of having his kid blow up the wall and slip him out under the cover of night.