WOW this sounds exactly like my MIL! Yikes.
She would beg to change diapers and do a happy dance when she could! She was so disappointed that we didn't just give DS bottles and want him to stay overnight at her place ALL the time. In fact, because he was breastfeeding and never sleeping through the night, he actually didn't stay overnight with her until he was 2 years old. And even then I had to put him to sleep and come back super early in the morning. We had her babysit for a couple hours at a time sometimes.
I thought her behaviour was really strange at the time, but now that DS is older and we have had more time with her as a grandma a lot of things have become clear (her personal happiness depends on DS and DH entirely too much because of problems and failures in her own life and personal relationships) and we just recently had a big blow out over Christmas. MIL's crazy side when it comes to DS totally reared its ugly head. Fun times.
I totally agree with a PP- breastfeeding will be your saving grace and an easy excuse. And YES make sure you and your DH are totally on the same page and that he doesn't cave and give more than you are willing too.
After that it'll just come down to setting really clear boundaries. You are the parents. One thing that I've found is so cool about becoming a mom is this new sense of strength that you get- YOU are the best and strongest advocate for a tiny person that can't speak or fight for himself. You are the best person to decide what he needs and what is best for him.
I think the older generation don't really get that with breastfeeding and attachment parenting, you can't just hand off the baby for days at a time (or even hours). And that's really different than the experience they had I think. I know my parents used to leave my sister and I with our grandparents for weeks! We certainly weren't attachment parented.
Anyway, good luck. It can be hard and honestly, at least with my MIL it hasn't gotten that much easier yet. And we have another baby coming. Baby-crazy grandmothers are a handful.