Sure. Stop it. If someone does something that makes you feel awkward ALL THE TIME would you look forward to seeing them? Just hug the kids for now and stop the affection with her.
As far as the concert: Do NOT let her go with that guy. Try to stop that.
Here's my experience that I hope you can benefit from: My husband wanted a "break". That turned into a separation, that turned into "I think I want to date other people. I don't like to be alone." Like a desperate idiot, I agreed to let him date other people because he said he needed to see what else was out there. HUGE regret on my part.
I didn't know it then, and I would have denied to everyone, told them they were wrong, but his EA had already started and that's who he wanted to date. Fortunately for me, the OW did NOT want anything to do with physically, so it stayed a short lived EA. But it happened, and it still hurts. Working hard to learn how to let it go.
Now in the meantime, we've made great progress from Christmas when he got me NOTHING but bought her $100 earrings. OH, and he was saying at every opportunity in many different ways the marriage was over, move on, divorce, divorce, divorce. And he was mean. Now, he doesn't use the D word but he also hasn't said "Let's work this out" either.
I live by this: Don't believe anything he says and don't believe 50% of what he does. People who are confused say some crazy crap, so I just don't give him the opportunity anymore.
Oh, and don't move if you don't want to. She can go.