We rent a townhouse now. We didn't wait for the bank or the sheriff to throw us out. Once we made the decision to go into foreclosure (situation similar to yours), we used the money we would have paid on the mortgage to move while we still had good credit. (It takes a few months for the foreclosure to hit your credit record.)
As for being in a home, you can still rent one (if it's in your price range). There are also people who are trying to do "rent to own" deals because their houses aren't selling, so that could be an option if you found the right homeowner/situation.
If you take control of the situation and prepare the kids for it, then you should be fine. It was so stressful to move (and we did it without kids!); however, knowing that we were working "the plan" made it a lot better.
After 3 years, the foreclosure comes off of your credit report. Three years isn't really that long.
I also know a couple who has 6 kids who went through the foreclosure process and they found a house for rent and the kids are thriving now.
Good luck to you.