Its so hard as a single parent to go to rehab and worry about everything else!
Be careful with your ex-husband. You have full custody of your kids right? That's what I'm saying. He might use it against you later if he truly knows that you will be in rehab. Not only that, it is not good to be "in debted" to him. I know how that is too.
Short term disability pays higher than unemployment. I don't know how much that is in your state. In CA- its $350-400/week Not only that, you can be on disability for a while, no? Like, few months at least.
Now who will be watching your kids? Can you borrow money to pay the rent? If you can, why don't you post date a check to your landlord now so you won't physcially have to be there to pay your landlord.
Another suggestion, maybe explaining your situation to your landlord about your situation. They can be compassionate and understanding too.
Maybe you don't have to go for the full 32 days. Maybe 25 days so you can make ends meet. You are a working single mom!
Good luck. Take care.
Love from Cali