A gran is entitled to the normal respect and politeness one would give to any house visitor. To my mind that doesn't include consideration for her expectations with regard to my new baby (supposing I were the new mum).
What I'm saying is exactly the same attitude that I had towards my own daughter, including in my house rather than hers. In my view the new mum is entitled to every consideration.
A visitor, especially a visitor one hardly knows, even if she is one's husband's son, is entitled to no more than common courtesy and civility. If she expects more then, in my view (and, yes, I know others think differently), she expects too much.
So, yes, I guess I'm saying that I don't think the gran's feelings about the baby in this situation need to be considered. The new mum's are paramount. Even my mum understood that and she is not the most sensitive person I've ever known.