She'll need your DH's consent to change their names or get passports, regardless of who has copies of the BCs. You might be hearing from her lawyers if she wants to do either and he doesn't want to consent.

I'm not sure why she hasn't applied for her own copies. Perhaps she doesn't realise that she can do that? (Although the application process can be a little fiddly).

And whilst I can see why your DH doesn't want to hand them over, I can also see that she wants them because he has them, and he won't hand them over because she wants them...Yet both of them could apply for extra copies if they wanted to.

I don't think this will be the end of it...which is sad for everyone.