Acting ugly, exposing, confronting with a MLCer, strengthens their resolve. It shows them the you that they are leaving and proves to them they are making the right choice.
An example of a healthy boundary (way to deal with it) would be "as long as you are involved with OW, I cant have sex with you. Or share a bed, or whatever works for you.
I will caution you though, if you cant set a boundary that you can live with, dont bother. They will test you and if you falter, future attempts at boundaries wont be believed.
You are so early in this. At this stage its hard to know what to do.
Guard your self esteem, heart, and health if you choose to continue to be intimate. If you can continue that part of the relationship with no expectations that it means anything and without damaging yourself, then i cant say not to at this point. You will know if you need to make changes.
"Acceptance doesn't mean resignation. It means understanding that something is what it is and there's got to be a way through it."--Michael J. Fox