Whatever happens during a separation sets up a precedent and an expectation for the divorce. I moved out (at X's insistence) and had my boys on alterate weekends. But this was OK with me because my X is a SAHM and I wanted her to keep the house and for the boys to live there if we did get divorced.
It sounds like you don't necessarily want full custody. Presumably an equitable division of property as well, meaning sell the house or one buys out the other/ offsetting assets, whatever. If that's all OK with you, then there's nothing wrong with the arrangement. I've even heard of couples who get a small apt for them to alternate with the house.
But, examine your husband's motive for a second. He knows that if he moves out, and sees the kids less than half-time, that sets up a presumption that you will have custody and he will pay child support. If he wants joint custody and no child support, then he would have to get a place that was suitable for him and all the kids. He doesn't want to have to go that far just yet.
For him to live at OW's one week, and then be at home with the kids for one week (without you)is just what he wants for now. And I can assure you that there is an OW, otherwise he would be in no hurry to leave. If you can point to a time that things suddenly got worse between you, the first time he didn't want you to touch him, that's when the A started.
Another clue: Does H care which week is his first week at the house? My guess is OW may have joint custody of her kids, and so he wants to coordinate the "child-free" time. He probably said the "first of October" because it sounds like a natural starting point, but it will line up with her week w/o kids. Tell him you want to be gone that first week, and see if he objects.
If I were you, I wouldn't agree to go sleep at a friend's house for a week at a time every other week, just so H could visit with his kids without you there. How do you benefit from this??
