Advice Needed- setting boundaries

[Sam3]

An update-
Thursday afternoon H texts me that he would like me to bring kids down to where he works during the week & stay with him at condo. Asks me if I would like to come to. He says he wants to see kids & work on things with me slowly.
I tell him the kids would love to spend some time with him & I can even stay at a hotel.

We go to a 2 hour MC session on Friday. Where he admits that he took OW on his "fishing trip" with buddies a few weeks ago. He says she stayed in his room, slept in his bed but they did not have sex. He says they kissed. I don't believe that. I told him that I was no longer "scared" of what he would do, if I did xyz. So he says "okay, if you want a divorce than lets do it."

Because he had OW listed in his phone under a guys name. MC asks if there are other women under different names in his phone- he says yes. That is hanging out with several women. He does not want a relationship with any of them.
He stated again that he wishes I would let him go.

I'm totally disgusted. Because we both said in MC that we feel like we can't be ourselves around each other. MC suggested we try to be ourselves.

I was very pleasant over the weekend. Because previous weekend I was a super b*tch. Because I could not stand the texting constantly in front if my face.
We went to lunch to lunch as a family on Sunday afternoon.

Sunday evening I asked him if he decided if he wanted me to bring the kids down. He said "no, I think I will just do a vacation with them by myself." He said he was fine with putting some "feelers" out to reach out to me until we went to counseling and he felt attacked.

I felt like I had to have another relationship talk with him before he left for the week. So I told him again, (told him same thing 2 weeks prior)
That he was free to leave. I told him i have no control over him, but I do expect him to respect my boundaries about contacting OW from our family home.
He did not have to come home on the weekends. We would all be fine.
He told me I could have the kids for 4th July.

I went on to tell him, that it might be best if he did not come home. I am not so sure about my feelings for him. I told him that I understood we had problems in marriage prior. But starting relationships with other people only adds to the marital problems. (Our marital problems being, that he feels like I got pregnant with baby #3 on purpose, that I don't show him enough affection, and I just didnt know how good I had it)
I did say I deserve a husband that would tell me we had marriage problems. He said he tried by asking me why I don't ever hold his hand etc.

It's very important to him that we remain friends and on friendly terms. I told him Im not sure i can ever be friends with someone who put no effort in to saving our marriage.

He says that nothing is changing in his life. He's going to do his own thing during the week at work and still come home on weekends to see kids. I feel like I can't really kick him out as Im a stay at home mom & he pays all the bills and gives me a weekly allowance. But if I'm still here taking care of kids on weekends, he's here to do fun stuff with them. Nothing is changing.
I know it's easier to DB in the same house but I feel like he needs to see we aren't all sitting here waiting for him to come home. And then hang out & chit chat like normal. He sleeps in spare room since we brought Baby #3 home from hospital.

He said he still was not sure if things were over with us. I feel like he wants to do what he wants for however long & then maybe or maybe not decide to be my husband again.

Do I leave our house on the weekends & leave him with all the kid responsibilities- dinner, baths etc.? because right now I'm still doing everything.
I feel like he is "cake eating" big time.

He insists on talking to me at night after he talks to kids, because they are so little he doesn't understand what they are trying to tell him over the phone.
I try to answer his questions nicely, not engage in additional questions & keep it short.

What's the right thing to do? Again, he's living 2 lives and I'm still taking care if kids so nothing is really changing for him.