There needs to be some serious soul-searching and sacrificing that will need to be done. Many times in order to get ahead (especially financially) you have to take a step "backwards". Walking away and getting a bigger house for the same price is not an option IMO. If you can't afford the price of the house now, extra square footage is not going to change that.
I can tell you that "blowing" your credit not only will not get you a bigger house, anytime soon at least, but it will likely set you backwards financially until you're almost ready to retire.
It's good that you don't have cc debt but you mention that you are living within your means but have no cash savings. It's impossible for anyone living within their means to not have savings. Within your means does not mean you can pay your bills. It means you can pay your bills, save for retirement, and have 3-6 months emergency funds. Emergency funds are crucial when you have a house and especially children. I don't mean to sound preachy but I am only 25, put 20% down on my home, one income that's under 30k (gross) a year, and still manage to save a minimum of $250/ month. Granted I don't have student loans, and I do have a car loan, but I don't have a $310k mortgage. You mention you have car loans on two cars, with the $600 student loans. Do you need two cars? You could sell one, save the money, and save even more on paying insurance for just one vehicle and loans for one vehicle.
It seems like you want to move on with your life with no sacrifice or consequences and pick up where you left off, actually better than where you left off. Meanwhile people are selling their cars and taking the bus, or using one car, some folks are moving to less expensive areas, downsizing and other extremes. And if you do happen to get your bigger house that's the same price as the one you cannot afford (I am saying you cannot afford it because even though you are paying your mortgage, you have no cash savings which astounds me for two people with great jobs) your "blown" credit will make that bigger house even more expensive because your interest rate will be sky high.
I also want to say that a house should not be seen mainly as an investment. It wasn't "throwing your money" away when you signed the loan.