I see a couple of issues here and I will offer my opinion and you are welcome to give them consideration or to throw out my ideas as not suitable.

Little girls should be raised to stand on their own two feet and not to run to the nearest man (not even daddy) when they can solve whatever the difficulty is on their own.

It seems to me this issue might be about manliness and masculinity and how it relates to the less-powerful, male-dominated, has fewer rights female than about fatherhood, per se.

Your wife managed to escape your father-in-law's domineering clutches and now pop-in-law sees another chance. I think you're right to put a spoke in his wheel. But not with regard to just the little girl; but with controlling your lives on holidays and other times.

You and your wife should be making your own life as a family unit. Talk these things over with your wife. Don't ask her, but tell her, that you want these special once in a lifetime moments with your daughter just as she should be having mom-daughter moments. You should be working with your wife to manage your overbearing in-laws. (on both sides, if necessary).

All of that said, grandparents should be a part of their grandchildren's lives; but as grandparents. Encourage the grandparent moments, but don't allow your wife's father to continue to dominate your family.