No, it is never impossible to get credit so long as there are no price controls or quotas.
In most of the United States, the impetus for housing is so strong that it's one sector of credit that has nearly no price regulation, price in this case being interest rates.
Corporate banks will not touch you now because Dodd-Frank now makes them liable to you and investors if you default on the mortgage. Also, Fannie & Freddie, who ultimately finance most mortgages in the US now require banks to buy back loans if they fail, so banks are only financing the most creditworthy.
All is not lost because markets are like rivers if not fully dammed: they find a way through.
In your case, you can get a fully-financed mortgage if you're willing to pay interest rates probably double what you could otherwise get in the market with good credit.
If the foreclosure process is quick and benefits the lender more in your state, the interest rate will be even lower.
Your creditors will most likely be individuals you find at mortgage investment clubs and religious institutions. If you shop around, you'll be surprised at how low a rate you might get.
Also, since the cost of your prospective home is so low, it's very easy for an investor flush with cash and few investments to take a flier on a mother committed to her children who only needs $50,000.
The FHA has been vastly expanded, and since your individual credit is clean, there may be a chance to get financing through it, but be prepared for red tape.