Help Family Secure New Home Amidst Crisis

My family and I are being evicted (since our lease was up) because they want to turn the place into townhomes. My husband has gout which limits his physical capacity for work, I have been on disability for a decade due to severe mental health problems and my sons' are both special needs (autistic and bipolar with crippling anxiety bordering on agoraphobia, plus body dysmorphia as he is trans.) We were actually in a good place when we moved in last year, as I had gone back to work, and then a series of very unfortunate events occurred.

I found a place the right size that would be much more affordable for us, though does require us moving further than we'd like. But they require the first and last month's rent plus a full month's security deposit. Overall this move will save us about $2000 a month, but having little warning and already running so close to the bone we had no chance to save up. They want us out any day now, and we have no way to come up with 3 month's worth of our new rent immediately. Neither of us has a lot of friends, and almost all of them are broke. Neither of us has family to fall back on as we broke with them after lifetimes of abuse towards both of us when they refused to accept our son's transition and tried to interfere with his brothers' acceptance of it, telling them not to call him by his pronouns or new name. We can get into a really good position with this move if we just can get the $4200 to move in right away.