Kind of going off that bastard ask you received, why do you think (so far as we know) Elaena Targaryen was never treated poorly despite having twin bastards from her affair with Alyn Velaryon? If she had been shunned at all, that seems like something that would have been pointed out, but instead the fact that she had bastards is merely a passing mention. Did Daeron prohibit negative talk about her? Was she left alone because she was so beneficial in her de facto position as Master of Coin?
Wellllll… you have to consider the timeline, it helps give context.
Princess Elaena Targaryen was freed from 10 years of imprisonment in the Maidenvault in 171AC, at age 21, after her brother Baelor’s death. It’s not certain when she began her affair with Lord Alyn Velaryon (nor whether his wife Baela Targaryen was still alive at the time), but she agreed to marry Lord Ossifer Plumm in 176 AC, a year after Alyn was formally declared lost at sea. Elaena’s cousin Aegon IV became king in 172 AC.
So I’d say it’s most likely that Elaena and Alyn’s affair primarily took place during the early years of Aegon’s reign. And after King Viserys II’s sudden and mysterious death, and then with Aegon the Unworthy on the throne… going through one mistress after another (the Bracken scandal was in 172 AC), sleeping with every maiden and whore and married woman in King’s Landing (that the gold cloaks would bring to him)… quarreling with his son Daeron, accusing his sister-wife Queen Naerys of adultery… attempting to start a war with Dorne in 174 AC… Well, with all that going on, a love affair between a princess and the hero Lord Admiral Oakenfist probably wouldn’t have even been noticed.
Also, this might be a bit ficcy, but I’d bet that Elaena only discovered she was pregnant after Alyn set off on his last voyage. She had hoped to marry him, probably on his return– it may have been that they were even formally betrothed before he left. I’d think a major reason she held out for a year after he was declared dead was not just the hope that her greatest love would return to her, but also the hope that their marriage would post-facto legitimize their children Jon and Jeyne. Alas, it was not to be.
But note that it was Aegon who insisted that Elaena marry the elderly and wealthy Ossifer Plumm. You can imagine the pressure he was bringing to bear, as she was unmarried with twin bastard children… maybe Aegon was the one who shut down any potential negative talk, for her cooperation? Maybe he even offered a carrot of legitimization? Also note that it was Aegon who almost certainly fathered Viserys Plumm on Elaena after Ossifer died on their wedding night… and while it’s been speculated that Aegon was “comforting a widow”, or that she was tempted because Aegon was still handsome and not at all gross yet… maybe it was a little more hinky than that. Maybe there was pressure there, too. :/ And considering that the infant Viserys was used by Aegon to take the Plumm wealth and lands away from the more definitely legitimate heirs… well, whether Elaena had a real choice in the matter is something, knowing GRRM, that I’d be hesitant to say.
But after that extremely brief marriage and the birth of Viserys, it was at least another 7 years before Elaena married again, to Ronnel Penrose, King Daeron II’s master of coin. (Daeron came to the throne in 184 AC.) So in case you’re wondering why Ronnel might have been willing to marry a woman so touched by scandal (or even why Ossifer was), you have to remember that it had been a pretty long time since those scandals. Also, note that Elaena was really the only marriageable princess the Targaryens had to offer. Rhaena and Baela of Pentos (if widowed) would have been in their late 60s if not dead already, Naerys was dead, Daena was almost certainly dead (as she drops out of the narrative after Daemon’s birth, therefore GRRM=“she died”), Rhaena was a septa, and Daenerys was only 12. (Also Daeron was setting up the Dorne betrothal/treaty with her.) And a princess is a princess – and Elaena grew more beautiful as she grew older, per GRRM. When Daeron requested the match, I doubt Ronnel made even a peep of protest. And even though the marriage was by royal command, Elaena probably found Daeron’s requests far more pleasant than Aegon’s.
So, for the years of her second marriage, Elaena was entirely publicly respectable. She had four perfectly legitimate children. (And after her seventh child, she said if 7 was good enough for the gods, it was good enough for her, and stopped.) Ronnel had a perfectly respectable job as master of coin. (Never mind that Elaena’s brilliant mathematical mind was doing all the work.) And Daeron’s court was such a change from the decadence of Aegon the Unworthy’s, I doubt anyone would have snarked at Elaena’s (ancient) history with Alyn. Even Elaena’s son Jon Waters became a famous knight during this time. (He would have been about 12-16 at Daenerys’s wedding tourney in 187 AC – the final tilt was won by Baelor Breakspear over Daemon Blackfyre, but I bet Jon performed pretty well.)
By the time Elaena was widowed again, I sincerely doubt anyone spoke negatively about her at all. I mean, there was Bittersteel and Bloodraven and Shiera’s triangle, then Daemon’s rebellious rumblings, then the First Blackfyre Rebellion – the court gossips would have had much more interesting things to talk about than Elaena. Her romance and marriage with Michael Manwoody was likely a quiet love of 40-somethings (he played the harp for her, gosh) – perhaps not the kind of thing singers call passionate, without that touch of scandal they enjoy writing about, but just the love she needed after all that time.
Anyway, to sum up – even though a noblewoman having children out of wedlock is normally a huge problem (let alone a princess), Elaena Targaryen’s scandal with Alyn Velaryon was probably overshadowed by Aegon the Unworthy’s far greater scandals at the time. By the time his reign was over, everything was so far in the past, and she was so necessary for marriage diplomacy and her skills with money, that none of it was likely to ever get in the way of her success. I hope that helps!