If I read right, your ex left you twice and she cheated?
It doesn't really seem like you're ex cared much about your feelings like you did about hers. But all that doesn't matter because the relationship is over.

As far as "her friends" reaching out to you to hang out, she has no right to tell you that you can't. It is your choice and their choice to hang out or not.

And for this "new girl", it's always hard to start a new relationship with an ex's friend because it comes with a lot of baggage, insecurities, and unwanted drama. Your ex could freak out and make both your lives miserable or she could just get over it. You never know. And I know you said the new girl asked you to stop, you could try one more time if you think she's worth it. If not just move on, live your single life and enjoy it.