Could you live with the co-sleeping if you still had a normal sex life?
Cause that, imo, is not so much a cultural issue..after all, there are millions of American co-sleepers.
If she would agree to working on your sex life, would you be willing to give co-sleeping a few more years?
Cause, honestly, your kids are getting to the age where they will naturally outgrow it at some point. In this country, kids do not sleep with their parents as teenagers and yours won't either. In principle I have nothing against co-sleeping and even think parents who do it are quite devoted. I couldn't even stand the phase when our kids were newborns and slept in between us for a week or two. H and I are both very light sleepers and it was the equivalent of all of us being up the entire night. In fact, I have a difficult time sleeping with just H..he's horrible to sleep with!
Anyway, you might be going up against a brick wall in trying to eliminate the cosleeping and it probably isn't the core issue anyway. What if you successfully get the kids in their own beds and she won't sleep with you anyway? In fact, it sounds like this is what would happen because she'd be angry at you and lonely for the kids.
But I agree you need to do something--no sex for 4 years is ridiculous.
Good luck and stand firm in what you want and need out of this marriage.