My long-inactive brother and his non-jw wife went through something like this with my mother when their daughter was about 4 years old.
My mother had an on-again/off-again disowning of my brother for leaving the 'truth' when he was 16. She rescinded the disownership when it served her needs and it was extremely exhausting for my brother. But he played the game until...
My sister-in-law was brought into it. Mom wanted SIL and the grandbaby but not my brother. My SIL put her foot down and stated in no uncertain terms that if Mom didn't have a son, then she didn't have a DIL or granddaughter. They were a family and would be accepted as a family or not at all.
14 years later Mom moved in with them. (Not for long, but that's another story that's not really mine to tell...)
Others here have taken a similar stand. The JWs can't have it both ways. Plus, as the baby gets older, it should be unconscienable to allow a grandparent to insinuate that the child's beloved parent is somehow evil and unworthy of the simple dignity of a greeting from their own parent.
Congrats on the Baby!! Good Luck with the Dub-Grandmom.
-Aude.