Do you get any sort of financial aid or loans? I think the only way we are going to get by this year is that my husband is taking out student loans - he is going back to school full time, and I am only working part time at a job that doesn't pay very well. Debt does suck, but its a trade off if you want to be a little more comfortable.
And maybe you might be eligible for more state benefits depending on where you live - assistance with electricity/heating, healthcare, etc? And I'm sure you've figured out a budget the best you can, but once when we were struggling we moved out of a really nice apartment into one that was several hundred dollars a month cheaper. Sure our new place didn't have a pool and I had shared laundry and other annoying things like that, but it was totally worth it to have a more affordable place so we could actually spend some money on fun things and necessities like clothing.
If you look into your community calendar in a local paper or something I bet you can find lots of really cheap or free local activities. I think city programs will offer lessons for swimming and art and things like that for very affordably sometimes. And going to local festivals, hiking and walking, camping, and other sorts of activities might provide some entertainment for your family without being very expensive.