she loves me but not sure she want to be with me and
she need her space. So I offered to leave but she said it be better if we stayed in the same house for the kids and keep trying to work it out but we are no longer a couple
If she won't go to counseling, I think you leave to let the emotional dust settle, and give her all the space she needs to figure out how hard she wants to work this out. You seem ready, but she does NOT!
Sorry guy, but no way do you accept this "no longer a couple" but stay for the kids. You have been through enough, and settled for too much, to let her have that kind of control over the situation. She said your not a couple, so don't pretend. Children notice how parents interact, and that effects them as bad as a separation.
Either she does what it takes, or she doesn't but, why suffer over her issues, when she seemed clear to me. I think you just are enabling, and empowering more bad behavior, without resolving your issues together, that can benefit you both, through some very honest communications. I get she just had a child 6 months ago, your people don't like her, and she has been going behind your back for a year already. That's enough of that. Her commitment shows no actions from what you have written.
Give her what she asked for, all the space she needs.