Landlord of 20 years raising rent 50%, gave us 2 months notice.
For the sake of your kids, if you need help, you are welcome to reach out and contact me in PM. No promises, your situation seems, no offense, more and more complex the more you post about it. No judgement, there is clearly a lot of nuance to these sort of things.
If I were in your shoes, and I'm not, based on what you've said so far, it appears the best long term play is to take your youngest and move out of state. And see if your oldest can find a place to ride it out for high school, etc, etc. I may actually be the 2nd person in the thread to talk about this option.
In general, in situations like this, a lot of people want to focus on what they aren't willing to give up. That is burning time. The longer it takes to cross a certain mental/emotional threshold about the things you'll lose, the harder the logistics will end up.
My unsolicited suggestion to you at this point is to assess all the things you don't actually need to survive. I mean core essentials. I'd start selling everything outside of some very core needs. Whatever happens, you want to be lean and mobile. Odds are you've got two decades worth of stuff in that place, which is probably still a lot of stuff. You'll also want to cut off all your expenses down to rock bottom. Starting now. You can do this now, or you can do it later when it's ten times harder, but it's going to have to happen unfortunately.
What's happening to you here is happening to a lot of people out there. There are more complex discussions that can be had about it, but we can't have them here on these forums anymore. And I understand why that has to be. It's unfortunate in regards to some light discussion of actual NY public policy has some predictive elements that can lead to making a decision in one area versus another, i.e. what's the best percentage play as the entire housing market locally reacts.
In consideration of your children, you can reach out if you wish. If not, I wish you the best of luck as a fellow long time member of this community.