Good sir, you are willfully ignoring the fact that Jace, Luke, and Joffrey are all recognized Velaryons - no matter the truth of their DNA -, claimed by Rhaenyra’s husband, Laenor (and his father, Corlys, current ruler of Driftmark) as his sons and heirs. The King, Viserys, also acknowledged their legitimacy as members of House Velaryon. Which is why Corlys tells Rhaenys “history remembers names not blood”, and he declares for the Blacks. They are Velaryons, as Laenor was their legitimized father, and by all historical accounts, fall under his family tree.

Additionally, we all know they were plotting to steal Rhaenyra’s crown long before she had kids.