In your shoes OP I would go back to my old boss. " I kind of upset my previous employer by leaving with a month's notice to be a stay at home dad as they did have plans for me. "
He may be willing to help and it sounds like it was long ago so he may not be so angry now. Lay your cards on the table, your ex manipulated you and you made a big mistake. You are very sorry and you would really like to be considered for any new work that comes up.
I don't see why you need to only work four days s2 week. Can you not work five and see your daughter at the weekend? She will be st school soon , won't she?
If your ex works full time your dd will need childcare. But as you have learnt, to your detriment, about being the stay at home parent, so some childcare will be needed. I
Re yoir old boss, it's going to make you look a bit foolish but I would say it is worth a shot.
Your ex sounds like a bit of a nightmare bitch. Make getting financially stable a big priority. Why do you need a house, necessarily?
A flat or masisonetre would do fine with two rooms for now.
Tell yo your ex that you need to work to pay maintemance.
Is there is a chance you can work 5 days, M-F or whatever, see if you can see your child when not working. If you got a 5 day a week job that includes the weekend (hospital or hotel maintenance type thing, do they work round the week?) Then that may help your ex with child care as well. Weekend jobs might pay more.
Get your ducks on a row before you speak to ex.
Try and put the past behind you both for the sake of your child. If your wife likes going out then having you to take care of your daughter on the evenings could strengthen your relationship with your child and make s workable relationship with ex.
I'm confused when you split and how old your daughter is now.
Ignore anything I've said that is not sensible for you.
If your experience really thinks it's ok for your child to sleep in a van I'd keep working on getting settled because your ex may end up not having custody one day.
Lastly, any relatives who could help you out to get a very small starter home once you are in full time work? Mortgage is cheaper than rent but you need a deposit so I am thinking long term plans here.