Well, being in the same boat, I probably wouldn't. In fact, I haven't. My mother called me a few months ago and I didn't bother to call her back. I haven't spoke to her in 3 or 4 years. We didn't have a falling out prior to me no longer speaking to her, but I just grew tired of her behavior. I was tired of speaking to her when she was half-drunk or in a horrible mood because she was either jonesing or hung over. I didn't want her asking me to take my kids when she was in a questionable state of mind. She has seen my son a handle full of times, and as a matter of fact, the same thing for my daughter.
Here is how I see it. Her and I can go 'round the dysfunctional merry go round, speaking one day, not the next, but when kids are involved someone needs to get off. I'm trying to keep them sane. Since I cannot control anyone but myself, I was the one to end the ride. No one really understands what it's like to deal with a dysfunctional family member. It's not like you're dealing with an emotional healthy person here. It's not like you got into a little spat and need to make up. It's usually much, much deeper than that, and it needs to be addressed...sometimes by a professional.
It sucks, you may feel bad, you may wonder what if, but at the end of the day, only you know what that relationship is like. Unless your mother is trying to change her behavior for the better, you should maintain distance until you feel 100% comfortable that it's all good.
I am not one for being nice and keeping up appearances. If I'm done, I'm done. There is no, 'Sure we can meet." Meanwhile, I'm cussing under my breath, and checking my watch waiting for it all to be over. It's not worth my mental health. Kids can feel the tension. It's just not nice.
So, nope, if it were me, I would not let her see my kids unless she can prove she has changed, and that cannot be determined over dinner or on the phone.