@Tina Dupart I think you need to look at what's being offered here. Right now, your tenant owes you $10K. You are in the power seat. Your tenant is acting like they are in the power seat - I'll give you the 10K, if you let me stay 90 more days.
This, "I'll give you what I owe you, if you let me get into more debt with you," isn't any kind of deal.
Do you have their offer in writing? First, I'd ask for that. Then, I'd tell the lawyer that the lawyer just offered you a deal which was offered knowing you were under duress, which no judge is going to like. So, tell your client to pay me the 10K and get out on time with zero damage. That kind of deal is against the ethics required of the bar association and in my opinion, this lawyer could get into some deep doo doo.
If you still want to make a deal, which I wouldn't do - I'd tell them to forget it and pay me - but - you could tell them you'll take the $10K, but the rent going forward will be double.
A question - isn't there rent control there? When does that kick in? Do they have to be there 12 months? This also might be why they're trying to extend the lease period - maybe some laws kick in that protect the tenant?
You really just need to get rid of this tenant. Really, just tell this lawyer they just admitted they have the money they owe you and they need to pay you and get out on time.
And I really think you need to get rid of your property manager. You're doing all the work here and not collecting the rent from a tenant they shouldn't have rented to, because tenants who need co-signers are a bad risk. Why pay them? Fire them and tell them no, you aren't going to pay them a termination fee, because this is all their fault for not getting you a better tenant.
I'm really sorry you're dealing with this. But, sometimes you need to be tough. You have all the power here. Fire them all.