Tbh I do believe Rhaenyra had some deep seated issues with how the succession of the Driftwood Throne was being handled. It probably has a lot to do with Corlys not officially accepting any of her sons as his heir. As a result, it causes Rhaenyra to lash out with violence (she only reacts with violence when she feels like her sons have been slighted in some way).
Vaemond was outspoken about Rhaenyra’s sons being bastardborn, in his efforts to claim the Driftwood Throne for himself, and so she had him killed immediately:
She dispatched Prince Daemon to seize Ser Vaemond, had his head removed, and fed his carcass to her dragon, Syrax.
— Fire & Blood, Heirs of the Dragon
Addam was successful in taking the Driftmark inheritance away from Rhaenyra’s son. Although her sons aren’t declared bastards in this instance, the situation would still be quite insulting. GRRM himself said that Rhaenyra never forgets a slight. So it’s not surprising that Addam is ordered to reside at the Dragonpit, where he would be subjected to witness the punishment Rhaenyra has allowed for her enemies:
Traitors, rebels, and murderers would be beheaded within the Dragonpit, and their corpses fed to the queen’s dragons.
— Fire & Blood, The Dying of the Dragons
Then of course, there is Rhaenyra’s infamous crashout, which actually happens after Corlys brings up the Driftmark succession in conversation. Corlys never once gives voice to Rhaenyra’s sons being his heirs in text, which could be seen as a mark against their legitimacy. Yet he speaks easily of other bastardborn children being the rightful heirs to Driftmark. The book does a misdirect by making it seem like Rhaenyra is upset about her husband cheating on her with Nettles, but in actuality, the issue might have more to do with the same festering problem that’s been brewing between Corlys and Rhaenyra for years. I think there’s a much greater chance that Corlys’ words are what truly stung Rhaenyra more than some unfounded allegations about her well known adulterous husband having an affair:
Only Lord Corlys and Grand Maester Gerardys spoke in defense of the dragonseeds. The Grand Maester said that they had no proof of any disloyalty on the parts of Nettles and Ser Addam; the path of wisdom was to seek such proof before making any judgments. Lord Corlys went much further, declaring that Ser Addam and his brother, Alyn, were “true Velaryons,” worthy heirs to Driftmark.
— Fire & Blood, The Dying of the Dragons
Just as the succession crisis of the Iron Throne revolves around the conflict between Rhaenyra vs Alicent, the succession crisis of the Driftwood Throne does the same for Rhaenyra vs Corlys. I’ve said before that I don’t think it’s a mere coincidence that GRRM had both these succession conflicts taking place at the same time.
Ultimately, both Vaemond and Addam are casualties in Corlys and Rhaenyra’s power struggle against each other.