I get the "My house, my rules" idea. But I don't think it's wise to veer from a parent's specific rules for their child, as I think it can cause too much confusion and stress. For example, if the parents said, "no sugar," I wouldn't go ahead and just give the kid sugar "cuz they're in MY house." Also, when my grands sleep over, I adhere to their regular bedtime and so on. These things, IMO, aren't "house rules," like the "no hoods" rule that adaunas mentions, but childcare rules - and childcare choices are up to the parents.
If I really felt strongly that I couldn't allow a dummy or whatever, I would decline to babysit and only see the child with their parents present. As a parent, if someone felt they couldn't follow my rules for my child in their home, I would understand and respect that. But I wouldn't turn to them for babysitting.
However, that, too, is a parental choice. Since DD seems content to have the PGM babysit and has even accepted that they have different rules about the dummy, then that's that. While I don't think PGM should be interfering in DD's decisions about her child, IMO, it's DD's choice to let her (or maybe DD can't help it if she has no other reasonable childcare options).