Yes, Caley, I can see why you would be having trouble. Rent prices have increased over the past year or so as more and more families have lost their homes and are unable to get financing to buy something more modest. Therefore, there is more demand for rentals now than even a year ago. And the biggest demand is in single family homes. If there are credit problems on top of that, it would be most difficult to find a rental, and particularly a 3-4 bedroom in that price range.
Have you talked to and lenders who might specialize in loans to veterans or have special programs that might make it easier to just purchase something? Don't know how your credit looks, but that may be an option if it is not too bad.
Good luck to you and your family. If I can help, please do not hesitate to contact me directly.