Just my two cents .....
In my husband's family, they don't let go of the ex's either.

It's actually kind of neat to see that many years post-divorce my MIL is just as close to her ex's (my FIL's) family. My MIL is a very cool lady -- I often thank her for bringing my H into the world -- I wish more women would remember that simple fact when they speak negatively about their MIL's.... their husbands wouldn't exist without her.
Anyway, getting back to grandparents and babysitting...... I'm not there yet, but when and if that time comes into my life, I will babysit because I will be delighted to do so -- not because it's my obligation -- because, quite frankly it's not my job.
I didn't have the luxury of available grandparents to help me out with the kids. My appointments were scheduled on weekends so my husband could watch the kids. And we didn't have enough money to go out for dinner and such, so babysitters weren't necessary. We used to treat Friday nights as our "date night." The babies went to bed by 7:30 and hubby and I would enjoy a quiet candlelit dinner in our tiny dining room. It was cheap and very effective. Sorry...... drifting off topic here. My point is that I never resented the fact that my parents or my husband's parents were not available to babysit. I don't anticipate that someday my kids will resent me when I have to tell them "no."
I've seen friends of mine burn out from allowing themselves to be burdened with babysitting. Their own priorities are pushed to the back burner to accommodate their adult children's whims. Sometimes I bite my tongue -- other times I gently suggest to my friends that they need to start thinking about themselves. Sometimes our adult children need to be reminded they are adults. If we as parents don't remind them of this fact, who will?