I think there's room for a parent asking someone else not to give their child specific things, or kinds of things. I suspect that a more specific request, even if it's as broad as "no tablets or ipods, and nothing really messy unless it's going to be kept at your house for when they visit" might have gone over better than "please tell me exactly what you're giving the kids so I can decide if it's appropriate.

Though if it's gotten to "she thinks I'm a killjoy and I think she doesn't respect my parenting decisions" that's larger than Christmas gifts. And where is the children's father in all this?