Why does she ask when she knows she isn't welcome here?
Why did she undermine you? why did she deliberately try to supplant you in your daughter's affections?
She is, sadly, not a friend though from all you've written she loves you in some weird twisted blind way. But not in a healthy one, and she's too dangerous to let near you for a long time.
I don't think you should let her come and tell her that if she does, you will call the police. It will take a LONG time before enough has healed to meet her or have her at your house (whichever house that is).
Also, it sounds like your daughter doesn't want much to do with her, yes and I think you should take note of that.
When you see it's your mother calling, put your guard up immediately so that you don't get railroaded into something, like this, that is actually quite destructive. It's far too soon and she will almost certainly spoil your daughter's birthday.
She certainly hasn't had your daughter's best interests or true happiness at heart up until now and it's impossible to believe that's changed in a few short weeks.