Telling him that she’s got a boyfriend, but then keeping him on the hook and lying to you about it does not mean she’s not going to cheat.

She may not, but she lied and lied until you confronted her with the truth. Then blamed you. None of this sounds good.

You agree it's unhealthy so must agree it's also unfair, yet you still give her the ability to control it all. Where is your agency? And do you really think this dance isn't somehow affecting your children?

Take a firm stand. You make the choice. It doesn't need to be the end of anything other than this back and forth on her terms. It needn't be unkind or brutal, but come from a place of love and friendship.

I know you want to reconcile, but that takes two and a lot of work, and right now you have a co-parent who decides daily whether they're in a dating mood or not.

You ask about this calmly and from the position of "Isn't that the guy who was hitting on you?" If it is him, let her explain the rest.

Don't let her deflect or try to change the subject. It's small, but a fundamental breaking of trust, an outright lie, but why?