Hey Maybell - When you say you are going to need to rent for a year, is that because you need to be able to have child support in place for a year in order to be able to qualify for a mortgage?
If that's the case - I will just throw it out there that I think it would be totally reasonable for you to ask your STBX to co sign on a mortgage now to help you qualify. Then you can assume the mortgage on your own in about a year (there's a fee - and you have to make sure the mortgage you get is assumable). That's more or less what I did - I refinanced the house shortly after BD to get expenses down and will assume it alone once the year is up and I can count my child support as income.
If your STBX is sincere about wanting to help out and be reasonable - this would be a way he could help his children avoid multiple moves in the next few years. If he worries about being "stuck" on the mortgage -I'm sure the lawyers can come up with some legalese.
Sorry if this isn't the case - just wanted to throw it out there as an option.