I think you should give up on the idea of controlling H's sleeping habits based on his dating habits. H doesn't need permission to sleep in his own house, unfortunately.
Instead, thank him for sharing his schedule and then simply set a childcare schedule for the next week, specifying when he is responsible for DD. Then, ignore his whereabouts completely unless he does not keep up his end of the childcare arrangements.
If you are deadset on enforcing the date-then-no-roof boundary, you don't do it by arguing with him or trying to control his actions. You simply make the consequences for violating your boundary happen. What are the consequences?
-- will you start D? -- will you move out? -- will you contact OW and tell her that on the days she chooses to date your H, she needs to provide shelter for him at night? -- will you cancel all shared credit cards and close all shared bank accounts? -- will you simply state that you will note his lack of respect in your diary?
I guess you could clarify the consequences of him going on a date and then sleeping at home (though I would avoid giving a warning about any financial change.) Anyway, what exactly do you intend to do? What are the consequences for violating your boundary? And is this issue really what you want to use to force things? I don't really see why proximity in time between a date and sleeping at home matters. He IS dating, he IS living at home. I don't see how a few more hours between date and going home is a meaningful difference. It seems much more like you acting out and trying to control his actions.
If you have childcare arranged, then you can come and go as you please (him as well.) If you see that he violates your boundaries (whatever they are) under those conditions, then implement your chosen consequences.
