Cohen question

Trying to understand some rules here. So Cohens can’t marry converts. They also can’t marry non-Jewish peiple alrhough this would technically be applicable to all Jewish people.

So let’s suppose a Cohen marries someone in good faith that they are a Jewish person. They have two children, a boy and a girl (I don’t know if this makes any difference but let’s suppose). Years down the line it turns out that the person they married isn’t Jewish (their mother was adopted and their biological parents weren’t Jewish and they were only told now or something, this is the best scenario I could come up with, there are probably better ones). What happens? Is the marriage declared null? What about the children? What about the Cohen’s prohibition?

I know this may be a really weird one I just thought about ut and was wondering.