Wouldn't this be awfully confusing to a child. And even a child of 5 years of age can be made to feel that they are 'betraying' another family member by calling them something they most certainly are not!
I've got a feeling that this OW pushed for your child to call her parents granny and gramps. She's pushing, and in turn is pushing your H to tow the line. I would bet in his heart, he knows this is repulsively wrong, but has to keep OW 'happy'.
Myself, I would have a talk with my spouse about this, and in no uncertain terms tell him it is NOT acceptable to ask a child to do such a thing...especially when the parents are still married, and the OW is just that...another woman. Her parents are no more that childs grandparents than she is his wife! That's just my opinion, but then I have an extreme reaction to adults using children to manipulate others.
If OW is pushing this on your husband, sit back and watch the show. She will continue to push and push..and pretty soon he'll be able to open the door all by himself and walk out of her life at a fast trot.
Women are angels. And when someone breaks our wings, we simply continue to fly...on a broomstick. We are flexible