Hi H.,
Have you tried disputing the negative information on your credit report yet? If so, and I were in your situation, I too would try to hold off as long as I could and stay in the house. Letting your house go to foreclosure will surely seal your fate with regards to not being able to get another house for a long time. Of course, only you know your situation and if you can't feed your family, sometimes very hard choices have to be made. If you do decide to get rid of the house, I would at least try to sell it for what I owed. I may not be able to sell it at market, but hopefully be able to avoid a foreclosure. If your house isn't worth what you owe on it, maybe call the department of housing and urban development and see if there are any government programs you might qualify for. I know the government is trying to keep people in their houses so maybe they can steer you in the direction of how to keep from losing it.
If you've not yet disputed your negative credit items however, you may go to annualcreditreport.com and order your 3 credit reports once a year for free. If I were in your situation, I would take the time to review them when I got them then dispute EVERY negative item on them with the respective credit bureaus. I had two things removed from my credit report and it raised my score over 100 points. I have a friend that had 11 out of 19 bad things taken off just by disputing them. Her score went up too and she was able to refinance her mortgage last month. Once you've disputed all your negative credit items, and received confirmation from the credit reporting bureaus that your credit reports have been "corrected", see if refinancing might be easier. I don't know your credit score of course, but since I've seen how much difference taking 2 bad things off my credit report made, I'm going to be sure to check mine and dispute all negative items every year from now on. I've heard it doesn't matter if the items are accurate or not. You still have a right to dispute them if you want. It doesn't mean they will be removed. But it's up to the creditor at that point to contradict your dispute, and if they don't within 30 days, the credit bureaus HAVE to remove the negative info from your report. It's not a quick fix to your situation as it will take probably a couple weeks to get the reports and submit your disputes, and the creditors have up to 30 days to respond, so it would be like 2 months or more before you could re-apply for a re-finance, but I don't think trying to better your credit score would hurt your situation even if you still don't qualify.
Good luck! I hope you don't lose your home and can find a way to refinance soon so you can save some money and take care of your family.
Blessings,
N.