I can't quite see the problem in referring to oneself as a cat or dog's Mummy or Daddy as long as you do not get completely unreal about it.
It's how you treat the pet that is the issue not what you call yourself.
I refer to myself as my budgies mummy.
What decade were your grandparents born?
Desperately sad story of the assisted suicide of a grieving mother


absent. Thinking of you.