I am so not the expert here, but I would end it completely with OM before you tell H. But this doesn't mean 'in the future', it means now. I can tell you that just you having shower gel at his house (if my H had shower gel at OW's house) would make me lose it. If you want to work things out with H, you are going to have to shut OM completely out, NO contact. Yes, your feelings won't go away, but its a conscious decision we have to make as adults. A committment to your H.
I wish you luck. See if you can bump that appt for yourself, I think that's a good idea.