[The Squatter of Amon Rûdh]

Given the past relations of Gondor and Rohan, I should imagine that many families had branches in both kingdoms. Let's not forget that Morwen was herself Gondorian, and that therefore such cousins probably existed even without the marriage of one of her elder daughters.

I don't see Morwen's return to Gondor as a break with Rohan so much as a return to her own people after her bereavement. It's probable that her descendents in Gondor would be raised as Gondorians, but that would not necessarily present an insurmountable barrier. By all accounts, Mary Stuart was more French than Scottish, yet she was accepted as Queen of Scots without overwhelming dissent; and Charles V successfully combined the roles of King of Spain and Holy Roman Emperor for decades. Whether the same could be achieved in Rohan is, of course, an entirely different question.

Presumably any hypothetical Gondorian relative could in theory become King of Rohan. Although it would appear that they had no queens, descent in the female line seems to have been no barrier: Éomer himself was the son of Théoden's sister. The problem with this question is that there are too many imponderables: were there any Gondorian male cousins? Would they be accepted by the people of Rohan? Were there any eligible Rohirric heirs to the throne? What would have happened in the event of Éomer's death anyway? Since the death of Éomer before Elfwine's birth would leave no obvious heir, it's possible that the Rohirrim would select their king without reference to kinship, possibly choosing a leader for personal qualities. I don't think that this is a question that can be answered with any certainty, since it requires information that Tolkien did not see fit to record.