Hi C.,
Sorry to hear things are tough, I can totally relate because we have been throwing around the idea of having to file bankruptcy this past year too. Have you ever heard of Dave Ramsey? He has a free show on Fox Business News Network at 5pm and 9pm, or go to his website daveramsey.com. This guy gives great financial advice.
Let me warn you that I am not an expert in this field, this is just some information I have gathered along the way, so investigate it all yourself.
If you file bankruptcy it will not wipe out student loans, you will still owe 100% of them. In a Chapter 7 you can keep up to somewhere around $2500 equity per vehicle, or if you had 2 cars you could give one up and keep a $5000 one. I would advise you not to get this new vehicle. If you need a new car go buy one for an amount you can afford (ie how much cash you have on hand) for $2000-$3000. Look for something that runs good even if it looks like ****. Remember this car is temporary, to help you get back on your feet, then you can get a better one a few years from now. Do you have any other car payments? If so, sell that car ASAP and do the above.
Check your area for free preschools (Head Start is one where I live) or preschools/daycares that have a toddler class too and would let you volunteer for all or part of tuition.
You didn't say what your husband does or did - how is he taking a $10k pay cut if he has been in school? Can he keep the job he had? If not I'd take the new job and keep looking for an even better one. Can he take on any side jobs?
What can you do to earn extra money? Get a paper route? Work at a store (that gives you a discount on things you need like food or clothes) on the weekend? I always found waitressing to be pretty good money - maybe you could do that 2 evenings a week or something else part time to help out. What about watching someone elses kids, or cleaning houses during a time when your husband (or other family member) could watch the kids.
You also didn't provide very much information about your house and house payment. Dave Ramsey says your house payment should be 25% of your take home income. If it is a little more I wouldn't freak out, but if you are spending half of your income on the house payment you might want to consider selling it (or doing a short sale if values have fallen) and renting for a few years. Or not, but consider it in the whole picture.
Where else can you cut corners? Do you have a bread store in town - they are cheaper than the grocery store. Buy generic brands, a lot of them are just as good and you will figure out which ones are and arn't. Shop yard sales and second hand stores for clothes and toys, you can get name brand stuff in almost new condition for much cheaper. Do any of you have prescriptions you need filled? Check the paper for coupons, I have found $20-$25 gift card coupons at places like Walgreens, Rite-Aide and Safeway. Banks also run promotions - open a new account and get $100 free, check into these. Have a yard sale.
The most important thing is to sit down and make a budget each month, map out how you will spend every dollar before you get it. Obviously housing, food, transportation, clothing, are most important, but if you can budget in some "fun" money you should, even if it is $10 to go blow on espresso or makeup or something little.
I hope this helps, I'm sorry you are going through a rough time right now, but trust me, you are not alone!