Where will this end if I stay and don't meet her wishes?
This seems like an ultimatum with two choices if you stay- one being a marriage without sex, the other, a possible baby. Her refusal to use birth control has drawn the line in the sand.
The possible child is not the problem in this situation. Your concern is about bringing another child into a disordered relationship, and with a disordered parent. This is a valid concern but you are choosing to stay with this person and if she's refusing to use birth control, the result is a marriage without sex if you want to hold your boundary.
In addition, you are attempting to hold your boundary against your own biology- sleeping in the same bed and trying to abtain from sex while being sleep deprived. I'm not suggesting you don't have willpower or control but this isn't the best situation for overcoming biological drives.