I'm in the minority here, but I'd at least consider it. People make mistakes. It sounds like she has been petty and selfish in the past, and she has brought at least some of the alienation from her family on herself, but unless she's truly abusive I would be inclined to try to look past that and give her another chance.
She's getting older, and who knows how many more of these opportunities you'll have? My MIL is a wingnut. There were some times early in our marriage when she was truly awful to me (and more times that she was even worse to dh). She can be very selfish. But she loves our children, and I want them to have a relationship with her. She has come a long way (and truthfully, so have I), so even though we have virtually nothing in common and will never be *friends*, we can spend time together and even enjoy it on occasion. My kids love her, and I am glad I didn't deprive them of a relationship with her (not that you are). In the end, we're all she has, and I can put up with the annoyances in order to be kind to her. Even if she doesn't deserve it.
I'd certainly draw the line if there were potential for real harm to my children (or to dh or myself) but that's not our case, and it doesn't sound like it's your case either.
I would probably not jump right back into the week-plus stays, but maybe invite her for an extra day. "We were thinking of doing X on the day you have to leave; would you like to stay an extra night and go with us?" If that goes well, think about extending it further.