What a hard situation for you! I really applaud your attempts to heal your relationship with your mother so your children can have their own relationship with their grandmother--even if it seems nearly impossible right now.
Without knowing your mother or you, it is impossible to say--as others have--what her motivations or reasons might be, or jump to a conclusion about ending your relationship with her. I think our society has shifted dramatically over my lifetime (I'm 45) from one where we accept pretty much anything from family members and suffer in silence to one where we just "dispose" of one another, and I can tell you don't want to do that.
Maybe a good middle ground is to wait until a time when you are NOT needing her help in that moment, and you are feeling relatively good together--and she is feeling positively as well. If THOSE requirements are met, AND she then offers her help "anytime", then you might try, without any judgement in your voice (very important), just stating your observations...
"You know, Mom, you have said that to me many times, and I really appreciate your offer and your intent. It seems, though, when I ask for your help or your time, it is never a good time for you. Is there something you are feeling that I could help you with?
Let her answer completely, and try to focus on whatever feelings she is communicating rather than what she is or isn't doing for you. I suspect, if you try this kind of approach, you might find out that, while she is very much WANTING to be a "good mother and grandmother", there is something going on that intimidates her or makes her unable to actually DO what she says she will do. I would have to say that might also go back to the reason a mother would allow a boyfriend kick out her kids--not to blame at all, but instead to see if there is some lifelong insecurity going on.
"I would really love to have you around the children more, and I miss you as well. I also get pretty overwhelmed taking care of the kids, and it would be great if there were a way you felt good about helping. Can you tell me what you COULD be available for?"
I don't mean to give you exact words--you know your mother and yourself best--but if you can kind of defuse the feelings a bit you might both find out more about yourselves and open your relationship more.
I realize this could also just all blow up in your face--and it's ok to tell your mom that you might feel a little anxious about that.
If it doesn't work out, pick yourself up, brush yourself off, realize it's NOT you! And then maybe go find a counselor or mediator for the two of you so you can heal--there are some pretty big issues in your past.
Fiora