I just thought of something. (I really have been praying for you.)
How about a double-wide trailer for rent?
The last time we were looking for a place and money was tight, we did check out trailer parks. And they were cheaper than most apartment rentals. The only problems we had were location -- the most convenient (location wise) park was also on the edge of one of the worst cities in America (Camden, NJ) -- and we would have to maintain it. (No calling the landlord to fix something. It was our responsibility.) We were looking long-term, but trailers are like cars in that they depreciate quickly. They break down quicker than regular housing. We were considering a trailer for the rest of our lives, but your stepparents only need one for eight years. (I'm going with the youngest child is ten. I could be wrong there.)