I have a weird dynamic where my MIL (DH's mom) has moved to town full time. She frequently says she wants to "help" but doesn't usually make concrete offers and I think she is easily overwhelmed by our high-energy child (let alone adding in the baby). She is also frequently late so that makes it hard to count on her for babysitting. I haven't figured out if it's her personality or some kind of passive aggressiveness.

At any rate, I've let it go by not thinking of her as someone who can "help" unless it's an emergency (i.e. someone's in the hospital). I let DH make any requests for help, usually if I'm traveling.

I think it depends on the family dynamic. My mother desperately wanted grandchildren. Desperately. I have her some and my kids are her only grandchildren. I would have thought it very strange if she didn't want to babysit, etc after the big deal she made out of wanting them. And she does help a lot. I don't think she has an obligation to do it, but it would be weird if she didn't. I don't feel that way about my ILs. They love my kids, but they aren't nearly as hands on and that is fine.

I'd probably try to delve more into why it's bugging your husband so much. My husband is from a culture where it's a given that grandmothers watch their grandkids full time. My mother made no bones about it that she would never babysit. First, he never expected any full time help because we make good money. But he was a little sad at the missed opportunity that regular contact provides to building relationships. Fortunately my mom became more interested in spending time with grandson when he got older, around 3 or 4.

However, my mother is failing rapidly health wise. I am now much more a caregiver for her than she could ever be for my son. It is important to recognize limitations for seniors, and that many limitations are not always obvious.