I can't really think of any BL that matches your first description, though a few probably exist. But there are a couple that sort of go in that direction (coincidentally, or not, by the same author):
http://www.mangago.me/read-manga/sabita_yoru_demo_koi_wa_sasayaku/ (one of the MCs starts off in a bad relationship)
http://www.mangago.me/read-manga/escape_journey/ (this one is about two people who originally broke up because they couldn't make it work)
The first story in this one might meet your second description:
http://www.mangago.me/read-manga/renai_kidou/
Also maybe these (to greater or lesser degrees):
http://www.mangago.me/read-manga/mihanada_pectolite/
http://www.mangago.me/read-manga/bokura_no_shokutaku/
http://www.mangago.me/read-manga/friend_line/ (this one also starts out with one of the MCs in a bad relationship)
http://www.mangago.me/read-manga/eigyou_nika/
http://www.mangago.me/read-manga/saishuu_densha/
I'm looking for a bl manga or whatever where they don't fight to stay with eachother. Maybe the recognize that it wont work out for them or they just don't feel like fighting for the others love as much as they need to. I'm reading a student/teacher one rn and its pretty stupid how hard they fight when it wont work out regardless. I just want one where they recognize that.