One solution that has become popular around the country is for a homeowner to stop making payments, mail their house keys to the lender (known as "jingle mail"), and simply walk away.
Since a child's stability is being threatened, you need to reiterate the fact that no matter where you end up, you'll always be there for them. Try to maintain routine as much as possible, and if you can, keep them enrolled in their current school so that they have something familiar to turn to every day. For a child, their teachers, parents, and friends will be much needed touchstones in this difficult time.
The term "sub-prime mortgages" applies to those mortgages that were approved for those whom many banks would have turned down. This may include those with a spotty credit history or who earned less than most banks would think is the minimum salary requirement to be eligible for a mortgage. Some years back, many smaller mortgage companies sprang up with more relaxed requirements for those applying for mortgages, and the term sub-prime mortgages began to be used for these applicants.