I personally think you should be able to put your foot down at some point. My husband's father had trouble accepting he was a grandfather (apparently at 62 he was far too young to be).
My mother was the same Took ages to decide, in the end my boy was talking so we just taught him Nanna, and I think she's secretly pleased that he has a special name just for her, regardless of whether it makes her feel old or not
It was confusing enough in our family because DP is Papa (French for Dad) which of course I support, it's just others thinking I'm a single mum raising my son with my dad. MIL is Mammie (sounds like Mummy ) which I wasn't too keen on because of confusing the little boy, though ultimately it's French for Grandma so I don't want to ask her to change it, though I'm sure she would