What an intresting thread!
Here are my suggestions:
#1: You are a father. That always comes first, no matter what. If whatever plan you end up going with means you cannot afford as much as a chocolate bar for your child, then sell or pawn or do whatever it takes. No matter what, it is unacceptable to make that little girl want.
#2: This is America. Americans go forward, not backwards. Drive on, no excuses. I do not agree that you need to sell your Deuce or Vette EXCEPT if keeping them affects #1 above.
#3: Sell the Sonic. It is not anything you have an emotional attachment to, and it is an additional financial liability. Get rid of it and buy a decent used pickup truck, SUV or van that is dependable enough to use as a DD to go to work or visit your daughter. Buy it for cash if you can and maintain it yourself.
#4: That free room deal sounds fishy. Don't abuse it, make sure you do the work they ask, and pay some rent regardless.
#5: If that does not work out, keep looking for decent rentals/roomate situations. You will get good at finding them.
#6: If that fails, get a fugly used camper.
#7: Work out a financial plan for when, 4 months out, your income picks up. Stick to it until you are completely back on your feet and have at least $5K in the bank.
That's it.