You need more money. It is going to suck, but it must be done. You won't need childcare if your wife finds a job working opposite hours of yours. Yes, it will be a little painful, but it is necessary to dig yourself out of the mess you made.
Instead of your wife working, you can get a second job, if that works better. (Or better yet, you can do both.) A job as a server on weekends can pick up a surprising amount of cash. Does your wife have any skills she can parlay into a side job? For example, if she sews, she could make money taking in sewing projects, which can be done while she's home. She can easily hem a pair of pants while she's watching the brood. Do you have any skills you can use? Even if they aren't all that specialized, anything that you can do would help. Painting houses on the weekends would pay pretty well and doesn't require advanced training or knowledge. Put an add in Craiglist for whatever you can do. If you have any senior living communities near you, find a way to advertise there as a handyman. My parents live in a 55+ community and people will pay for shockingly basic things, like having someone come in a change light bulbs if it requires climbing a ladder, or having someone assemble furniture. Some even pay for a person to buy their groceries weekly, which it seems like your wife could do in conjunction with her own grocery run. (Do you only have the van?)
Sell stuff on ebay, Craigslist, etc. Whatever you have that isn't required for basic existence need to go if it will bring in even $1. You are in a red alert emergency situation, so start purging whatever you can and use that money to whittle down the debt.
Do some research and make sure the amount of child support your wife is receiving is far. If not, get it increased. The legal fees will likely be worth it. Also, you don't mention either paying or receiving CS for your kids, but you likely are doing one or the other. Again, make sure that amount is fair and is not, get it adjusted if you can. Also, if the custody agreement allows it, see if you can get the other parents to pick up more of those transportation costs. You agreement may stipulate that you have to do the driving, but if not, then see about meeting half way to hand off the kids, alternating who does the pick up and drop off each visit, etc.
Contact all of those monthly plans and see if they can budge at all. Even if you have to pay an early termination fee, if it is less than the cost of the rest of the contract, do it. It might seem like paying for nothing, but in fact it is paying for the money you won't have to spend on the rest of the contract.
Your comment on the food bill is very telling. You'd do it, except you don't know how much it will really help. Guess what; in your situation $5/mo would really help. So if you can shave $100 or even $50 off that food bill, do it. You created a situation where you don't have the luxury of deciding that a few dollars isn't worth the effort. So eat spaghetti at least once a week, and rice and beans at least once a week.
Also, it is crazy that you are driving that much for a job that pays shit. Look for something much, much closer to home. It isn't like you need to replace a 6 figure job, so finding something with comparable pay but a cheaper commute shouldn't be that difficult. Start looking now, and don't be all that picky. You can't afford to be picky. IMO, the thing you should be most picky about is whether the job has room for advancement and raises. Doing what you love is a great goal, but right now, you need to do whatever puts out some of these fires, and worry about feeing your passion when you can afford to do so, or with your second job.
Personally, I think bankruptcy is a cop-out unless and until you've tried everything. Opinions vary on this, but to me, when I commit to paying something of, deciding down the road that I don't want to pay anymore because it hurts is a cowardly, bullshit decision. It doesn't matter what the baks do, or what other people do. My word and my honor s about my choices, not about my choices compared to the bad choices of others. It sounds like you *can* pay your bills, you just don't want to because it will take 8+ years and more sacrifice than you like.