My daughter is currently dealing with this in 2nd grade. School's these days call it bullying and the offending girl gets a week's detention and has to write apology notes.
My advice to her was that her "friend," the mean girl, probably won't change. I told her to be nice to her, but not to try too hard to be friends with her because she probably won't outgrow it. This girl was picking on my daughter, who was the "new girl" at the beginning of the school year and another girl who entered the school in the late Fall. She either outright lied or took things out of context to have power over the girls and to keep "her friends" from becoming friends with the new kids - probably out of fear of losing them to the new kids. What got her detention was saying to my daughter and this other girl "I wish you were dead". Second graders haven't quite developed the skills of grownups.
But as I told my daughter, the woman you're dealing with won't change either, and isn't worth your time. She gossips to fill some void in her life, and she spreads rumors and lies to try to keep people as "her friends". The positive part that came out of the whole experience with my daughter is that my daughter learned she had the support of the other girls in the class (now that half the year has passed and they've gotten to know her instead of the bully's lies about her). They told her yes, XXX is mean. The girls haven't stopped being friends with the mean girl, but they see my daughter for who she is, not the mean girl's lies about her. I'm sure there will still be times on the playground where they have to choose who to play with, and those won't all go my daughter's way.
So, stick to your guns, don't stoop to her level. I would try to get together with the other mom's and kids. Try contacting them individually to set up a playground (neutral) playdate, not as a group. If the mom tries to give you the brush-off with a too-busy excuse, right then try to ask for a future date when she doesn't have something going on. If she again stalls, try to ask plainly that if there has ever been a time you have done anything to upset or offend her to please tell you about it. Tell her our children are friends and for their sake, at least, you would like the chance to clear the air. Tell her you really have no idea why it seems you are getting the brush-off from some of the moms lately and that you thought you were all friends. Make sure you don't single any person out, don't turn it into a gossiping session. Hopefully you will get some feedback. If you're not getting any, try one more time saying, I really regret the loss of our friendship, I truly have no idea what I may have said, done, or not done, but I thought we were friends and then things started getting weird. I hope for the sake of our past friendship you'll at least let me know why things changed. If there is one mom worth being friends with, she'll "hear" your words, even if she doesn't have the guts to act on them at the time. But making an attempt at clearing the air and addressing the situation maturely, will hopefully wake up the little part of her that liked you in the first place and you may start having an ally when you bump into the group (even if she doesn't speak out). OR, maybe the whole group are a bunch of catty bitches and it's better just to cut your losses now :) I would do nothing with the information that so-and-so has gossiped about every single member of the group, unless things get really ugly.
Also, the gossip may have assumed you agreed with everything she said about people if you didn't argue or dispute her when she gossiped to you. So, she may have "thrown you under the bus", if she got caught spreading a vicious rumor, and either said she heard it from you or that you agreed with her.