If this company offering the job is truely worth their salt, they should allow you all to find your own housing that would be more suitable size wise etc.
I dont think much of a company that would put someone in this postion to make these kind of decisions just to move to take a sticken job. There are plently of other jobs/companies out there in this big world.

I'm sorry that this new job offer has put your family in this awful situation.