You're doing grand!
I definitely think him renting something else is the best idea. It will not feel 'over' if he's in the annex and whilst part of you might be clinging onto that, it's not a good idea. You need it to be properly over to move forward. Try to fill the gap in the rental periods.
Rehoming the chickens will help if you can find a nice home for them.
Mediation is a complete waste of time when he's declared it over. There's not even any point to work towards a settlement because he's not going to play fair. Just file fir divorce siting adultery & naming her. You have enough proof.
I wouldn't put off selling the house either. The sooner you settle everything with WankerChops the better deal you will get. Plus the sooner you settle it, the less chance he has of having a baby on the way.
I know it bloody hurts, but it doesn't matter if they rent together or not, he's acting like a sad middle aged git...loves young dream . It's highly unlikely to last, but in the meantime you can't stop it, so try not to dwell on it.
If DD is a pretty sensible kid she'll be fine home alone with a friend or boyfriend a couple of times a month. (It wouldn't worry me them having the house to themselves, they're either having sex or they're not and having a house to shag in was never a prerequisite in my day - doubt that's changed any!)