Do you get anything taken out of your check besides taxes? The difference between your gross and net pay monthly is about $2900. If you normally get an income tax refund, perhaps you could change your withholding so you keep more money in your paychecks.
Which will cost more? Fulfilling the water contract? Or the fee (if there is one) for cancelling it?
I would definitely follow the advice you received about selling that car. I know you bought it recently, but if it's a mistake, fixing it now will be better than waiting until it depreciates further.
I know it's probably geographic, but the combination of your rent and utilities seems really high to me. $1300 plus ALL utilities in what you describe as a bad neighborhood is just nuts. Did you have a lot of opportunity to shop around before moving in? I don't know how many bedrooms you have, but for a family of four in a tight spot, you only need 2. I also don't know if you live in a house or an apartment, but apartments are usually cheaper and so are the utilities. You said your landlord is a nice guy. If he knows your situation, I'm sure he would be understanding if you needed to break your lease.
Congrats on taking control! You're going to get a lot of good feedback here. When I put up my journal, someone told me to sell my precious, precious car and I balked. A month later, I sold my car

All the advice you'll get here is worth considering!