Hi Amy,
What your daughter calls gf is not your hoola hoop. I could not call my step mom mother. I had a real hard time explaining to my children that grandfather's wife was not their grandmother and that dynamic. What they wanted to call her I had to accept even though I did not encourage it. After mom died, it became easier to allow the children to call her grandmother and for me to think of her as a second mom, although I know she will never replace mom.
As for Christmas, it's the tradition of Christmas you are establishing for the grandchild and your son.