My marriage is over

Two years ago I found out my husband was having an affair with a female coworker. Had been for 5 months. At this point my whole world fell apart, I had 4 small children and was a SAHM. I was heartbroken and betrayed. I thought he was my best friend. The following 3 months I worked hard with the help of my family to sell our home and settle debts so we could part ways. But all I wanted was him back, my home back. And my family back together. He split from his mistress and started begging to put our family back together. Be the dad and husband he should have always been. After months of persuading I finally agreed to ‘put our family back together’ we bought a house together and started to try to heal and forgive. I should add at one point we were living in a tent with 4 children and two dogs as no family or friends would put us up until the house situation was sorted as they didn’t think us being back together was a good idea and would not help us do so. Always 16 months later it turns out after I looked at his phone one night, that he has been talking to very young gay men (some as young as 18 and he is 40) and he refers to himself as Bicurious. We had a long conversation and now he want to go explore other options with other people. But wants us to stay in our house together with the kids and pretend we are still together for their sake. And also as he does not want to tell his parents that we have separated.

My struggle is that I feel staying in the house together is causing me so much In being near him. But I have no where to go. my children are at home here and it took a long time for them to settle in this house after what had happened. They saw it all and didn’t cope well. What should I do?

Tl;dr Cheating husband begged me to take him back. Only to cheat again, wants to live together for the kids under the guise of still being together but with the freedom to explore his sexuality and have sex with other people.