For better or worse, we have developed a routine where he comes over while I'm here to hang out with our D. He will stay until she goes to bed - helps put her to bed and all - then goes back to his parents' house. I've let this go on because this keeps me from having to tell my D. what's going on - she doesn't ask questions when she sees him frequently. He was working so much prior to this issue that she just thinks daddy's working on the nights he isn't here.
Last weekend when I found out OW was at our house, I flew off the handle and told him he wasn't welcome here while I was here anymore, etc., but then I think I just felt so awful about what that would mean for my D., I recanted. Today, for example, he was over most of the day.
I realize that this can't go on forever - but I really don't want to worry my daughter until I know it's for sure. I just feel so awful for her - this wasn't what I wanted. I wanted her to have a 2 parent family and not have to be torn between two. And selfishly, I don't want to give her up on holidays, etc. I'd rather share than not see her at all.