SheBear: When you talk to Foltest at the beginning of the game about Adda being alive I remember him talking about how Radovid can't be the heir to Temeria even though he is married to Adda. Something about how since Adda married out of Temeria she lost her inheritance(/the barons wouldn't accept it) as next in line for the throne, hence the confusion after Foltest's death.

I think he can only use his influence of Adda so far as saying "hey look, I am married to a Temerian, she is awesome; also I have a large army, I win." The Adda bit is more of a side note rather than the deciding factor of why he can try to take over Temeria.