What is Helen in... 6th grade? This drama is expected with young girls, even teenagers, but as mothers we have to show the right way to handle situations that come up. You have done that, Betty sounds like she has done that, Helen is a drama queen who wants the attention rather then the end to it, she also is living her childhood through her daughter. If Helen tells you that her daughter cannot play over at your house, don't play her game, just say sadly "oh I am sorry you feel that way, my daughter really enjoys playing with your daughter" and it leaves her with two choices... one, she can let her daughter come over and put this behind or two, she can keep her daughter home and try to explain it to her daughter why she is the one left out of the fun. What it teaches Helen is that she needs to think through her threats and controlling ways so it doesn't come back and bite her in the rear end.
I have never been one to give in to the black mail, choose my side or I won't be freinds with you, type of behavior. Real friends don't do that to each other. If Helen stops talking to you, it is her loss and your life will be much less dramatic... but I would keep inviting her to coffee and if she brings up the situation wanting you to take her lead, just smile and say "that is so in the past" and change the subject, don't give into it.
You are smart to know that children aren't perfect and your daughter could very well have done that, you took care of it and showed her that was wrong. It will make her a much better person then those who's mothers never think their children are in the wrong. I remember when my daughter was in the 6th grade and got into a fight with her best friend. I told her I would take them to the movie and they could work things out. She rode her bike over and everyone had a great time... but I also noticed that the bike stayed here for days afterwards. When I noticed it was gone I mentioned to the friends mom that she must have came and got the bike, her mom said "I don't think so" and asked her daughter. I thought someone stole it out of our yard and was ready to call the police when my daughter said "oh, I think I saw a bike like hers at the school" I asked my daughter if she took the bike there and left it there and she looked at me trying real hard to lie saying no she didn't know how it got there. I told her that she was to go to the school and get the bike, deliver it to the owner and if it is gone, she will give the girl her brand new bike! Luckly we are in a small town and the bike was there and she delivered it and she learned a big lesson on how not to behave. She was also grounded for quite a while. That is our job as parents, to teach our children how to behave and how not to behave, Helen needs to learn that by the sounds of it.