Genuine question here: do many grandmothers have the expectation that they will be "needed" and will be "helping to care for new babies" when the grandkids are born? If so, can anyone explain why? It's different if a new mom has twins or even more, but one reasonably fit and sensible woman should be able to cope with one baby, with just her husband to help. Husbands do so much more these days than they used to do. Many DILs are not even going to realise that MIL was expecting to help, and may even interpret constant offers of help as "she doesn't think I can look after my own baby."
OP, I would suggest you spend less time appearing to focus on the grandkids, and more time "spoiling" your DIL and son. Tell your DIL you're available if necessary, but that you know she's got this, and give her gift cards to some of her favourite "spoiling" kind of shops. Give your son something special too.
Every time you talk to them, ask them how they are first, before you ask about the children. If you want to go on an outing, some time after the baby is born, find something DIL would love, and suggest you and she go together when her son is at nursery, your treat. (of course, she would need to bring the baby, but don't make it about that.) Tell her you just want to do something nice for her. If she agrees, and has a nice time, she is more likely to invite you along some other time, when the whole family is there.
Don't make your relationship with your son's family all about the grandkids. You were a mother first, and still should be.