When xh and I separated he kept the house (I would never have been able to afford it) and we moved out of town and in with my parents. I was antsy to get out from under their roof and when we did, it didnt' work so we ended up back with them. The kids and I are in our own (tiny) place now and I'm going to school and it works because 1) xh actually pays his child support, which is a good amount, 2) I use the state's assistance program for child care to put ds in part-time preschool while I'm in class.
It's been kind of a blow to my pride to apply for some assistance programs but there was no other way, it won't be forever and I'll be on my own feet soon. I don't know how some women do it... child care is so costly that it wasn't even worth it for me to work full time and pay daycare.
I'd check what assistance programs your state offers, there's often heating programs for fall/winter, child care, and of course housing and food, etc.
eta: I also have a big office that I clean on weekends that pays pretty well for the amount of time spent. And the kids can come with me for this so there's no babysitter cost.