I don't know why some of you guys are looking at this show from Westerosi norms. I'm not from Westeros, I don't give a shyt about their norms. People in here calling b*stards nasty like they're actually disgusted with the idea. Like your sisters ain't got a bunch of little b*stards running around as well
Rhae's whole arch is based on breaking norms. fukk their oppressive society, I don't fukk with their rules.
Be a good uncle to your b*stard nephews and nieces
If Alicent was smart she would have taken up the offer to wed their kids together. What's important is power and influence, not 'what is right'. Tying the families together means the child of their children would have both of their blood and thus they would have equal influence over the future ruler. It was actually an incredible offer. Really, Viserys should have hopped his crippled ass up and said that as king he commands it. They're his children as well. That would have put an end to everything. Alicent is really just on some petty shyt. It's no longer about putting her house in a more influential position, she just wants to go to war and push Rhae out of the picture because she's jealous and resentful. She's losing the plot.
Another thing you guys are overlooking is that Rhaenyra has a male heir now, so to the realm her position is even stronger than it was before. All the worries about "a woman shouldn't sit the throne" are dampened a bit because Jace is looked at as the heir and future King.
Also, even if it was never made a secret that they were b*stards, once Rhae becomes queen she could legitimize them any time she wanted. There is precedent. I don't know if it happened with the Targaryans, but I'm sure other houses have had legitimized b*stards become lords in the thousands of years of history.