Cowgirl comes to mind.
But-in the interest of not-derailing the thread:
My advice is, figure out what you need to have some privacy first.
Seriously, I am in a V, as the hinge. My boyfriend and my husband are both straight and NOT interested in sharing me beyond the acceptance that I love both of them. We live together. At one point, with 5 kids.
BUT WE HAVE ALWAYS made a point of ensuring everyone has privacy and personal space and personal time alone. It is an imperative for sanity.
So, figure out what YOU need to change so that YOU can get YOUR needs met YOURSELF.
Stop focusing on THEM, HIM, HER etc-and focus on what YOU CAN DO TO CHANGE YOURSELF so that YOU are meeting YOUR needs.
After you figure that out-then you might be clear headed enough to address the rest of the situation.
Finally-at no point is it acceptable or reasonable for you to pressure him to leave his partner-REGARDLESS of what YOUR opinion is of their relationship. That is NOT your relationship or your business.
"Love As Thou Wilt"