You have no business dating right now. Leave it alone.
Quit waiting to be taken care of, take care of yourself.
H's behavior with the kids is not OK. Telling them to lie to you is not OK. Taking them on an overnight trip with OW right now is not OK. Trust me, I am not one who tries to get people to keep the kids away from OP. It is generally best to accept it.
But, this situation is too new and too unstable. If I were you, I'd text:
"I'm concerned about the kids. An out-of-town trip with you and OW is not appropriate for them right now. I understand that she'll be going camping with you, so I'll make other arrangements for childcare while you are on your trip. If I've misunderstood, let me know."
