"I think women are resources to be used up like a worn out dishrag and I'm pretending not to understand the problem with demanding their free labour till they drop dead" - just reminding you that I fixed your title for you.
So anyway, look after your own kids, it's your reponsibility. Never expect any childcare from anyone and especially stop demanding your mothers drudgery. They already raised you, job done.
For the excessively transactional amongst you - you have put yourself in an impossible bind. You think life is a transaction and your mother's resources, time and free labour can be owed out, in a transactional way.
Unfortunately for you, this means you owe your mother - forever. You can never, ever repay the massive debt you have incrued to her by raising you. That's how it works in transactional world. This also means you do, in fact, owe your parents aged care. No matter what you do, you can never repay the enormous debt you have to them.
Fortunately, life is not transactional, and I'm not a nutty self entitled twit - so I understand that no, you don't owe your elderly parents care. Although certainly any care you give them is simply a repayment of their endless time, money and attention to you, the fact that you are still alive is testament to their parenting. But still, it's not owed.
Your mother, of course, is not your servant, so stop trying to force her to do even more work. She's done her bit, say thanks and behave better.
Oh, and let's not pretend your mother was abusive to you, because if that was the case and you wanted her to do your parenting job that would make you a monster.
Think that about covers it. Look after your own kids, and stop demanding your mother's free labour.
If she offers, be very very grateful indeed.
When you stop making ridiculous demands on your mother (and it's not your dad you're asking, we all know that) and accept that she's not your resource to be redistributed, you'll turn into a much more pleasant person. So everyone will win. You're welcome.