I don't think you have to word it that way. If you're trying to set a boundary, why can't you say "As long as we're living together, I don't think it would be acceptable for EITHER ONE OF US to date other people." I think wording it as "I want this, and if you can't agree *I* will do this..." is putting an ultimatum on yourself and possibly giving him an out.
On the email from the COW (coveted other woman! ), do you know for a fact that she knows the whole sitch (that H is interested in her)? Sorry if you mentioned that earlier and I forgot. If so, I think your response is good- short and sweet.
Over the last few days, I've been thinking that my H is wanting to date other women (more COWS!). It's just a feeling I have and it's awful. Hugs to you...