Depending on the age of your daughter, she won't care. The only way she may care is if you send out negative messages about your mom.
From what you describe, it sounds like your mom has a lot going on...and is maybe suffering from depression or an undiagnosed mental illness? With this possibility, I'd just not worry about her not being available in ways you see fit, and let her live her life her way, and you continue yours, your way.
She clearly isn't going to change her ways, for you or anyone. And if it's because of what I suspect, change is probably not possible for her without some sort of outside psychiatric help.
I'm not saying cut ties, but perhaps start to manage *your* expectations, and just don't look to her for the kind of relationship you feel a grandmother should have with her grandchildren. She just may not be capable of this. She's probably doing all that she is capable of doing right now. It doesn't sound personal. It sounds like it's just her.
If it is important to you, for her to be present in your life, and you don't mind being the one to initiate visits, just accept the fact that you'll only see her once in a while, and when it works for you to get to her house or where you both feel comfortable. There is no harm in accommodating her to keep her involved in your life. It just doesn't sound like her behavior is a power-play, so I think this would be fine if visits with her are important to you.
As for the other grandmas, your daughter is blessed! She will have good relationships with them and that's okay. No need to compare your mother to them, or compare what she has or hasn't done with them. Just appreciate what she can and has done, and leave it at that. No need to harbor bad feelings or pass those on to your daughter.
When she's older, she'll understand that people have different needs, different personalities, different circumstances. The important thing is, I do believe her grandma loves her, and she'll know it.