I can see your ex’s thinking behind it. BUT I think that when sharing what is so obviously a special day, it’s very hard to not do something basic as a stocking that can be hung before he goes to his dads.
Fwiw, we hang out stockings very early on when we decorate. But we go to different family homes on the morning for presents and brunch. So my lo has stocking at home and at the family home we visit. To date no child has ever questioned it. It’s just what Christmas is! That same principle imo could be easily translated to two different parent homes.
