I wonder what the reaction would have been if you had politely declined, unless they were prepared to invoke powers and make it clear exactly which ones they were invoking and on what grounds.

I actually think the question about the ownership of the kids was an invasion of privacy, and if asked in front of kids, very insensitive. Not everyone has straightforward family relationships these days and it could be hurtful or embarrassing to discuss them. Just because you are dressed up in a black play suit doesn't give you the right to pry like that.