Nightwanderer most people I know who've stayed and shared with the ex after a break up have found it ultimately makes any breakup pain longer, or they resent having been forced into this situation as you can't move forwards (if you meet someone new where can you take them?) etc. I do know most have said it just doesn't work or works for very short periods only. I've heard horror stories of friends getting upset (but not wanting to) and the partner either comforting them or refusing to do so etc, either party has also felt pushed out (even if it was agreed to share the property) and there's an avoidance game. Not healthy all round.
What would be ideal is for OP to decide long term if she wants to stay in the flat can she get help either by guarantor loans or other monies from parents etc or her own finances and rent out second room. She can then move forwards stay single, meet someone new etc. her DH can be bought out. It appears she has a good job with support. She could also if need be get a second (part time) job to help towards her finances.
I don't blame her in a sense for cutting and running from the situation as ultimately she didn't want "the talk" or to confront him and it seems as if he didn't want that either. That's the only saving grace in their relationship as if it is really down to lack of communication then that's their main sticking point!
The way it's been handled on his side (and eagerness to see friends etc and presumably act as though nothing is wrong) isn't good going forwards though either.
I'm not sure if there is an OW either necessarily (in 2 minds) but I think her DH if they split would most likely find someone new quite quickly as some men are wont to do, OP knows this hence the running back and salvaging things.
The TTC would be another issue in their relationship though and if that does or doesn't work would they then be at situation they're in now?
All food for thought really.