If they don't honor it, they are in breach.I would write them a letter, with delivery confirmation (emails work fine, if that's how you've been communicating, as it has a date stamp on it), that says you only want that unit, so they can honor the lease or pay you back twice your holding deposit (or whatever you decide) by end of next week, as a settlement for breach of contract.

Today he told me he can't afford it, he can't afford the rent this month, and he got in an accident and he's waiting on a settlement...The good news is I'm in contact with a great property management company and I've signed an initial agreement to have them take over on June 1st.  

per divorce settlement/paperwork?

I can't really see her going to court either but she's already offered us an out of court settlement if we just give her back her deposit.

He is suggesting I offer a cash settlement and be done etc At this point I think they are waiting to see how best to exploit the situation.

One question I have about the child support, are you allowed to ask for proof of payment, not just proof of the settlement?

Get a good lawyer immediately.California hates landlords and loves poor tenants with personal problems.Yes,she can sue you and probably will win a settlement from you after driving you insane first.Doubt she can prove that air conditioning had anything to do with his condition but,California judges like to look for any excuse to favor tenants.Good luck to you.

Just don't give them any cash until they are out, have given you keys and sign a paper saying they are vacating and the terms of your "settlement."

A property manager would cost me $60-70k/year so for that cost I might as well hire my own local staff who can do the property management + other tasks outside of the typical property management scope (i.e. marketing for new properties, processing of new properties pre/post settlement, etc.).   

I'd tell them if they agree to sign a settlement letter, then I'd let the additional $300 they owed me go.