I'm sorry for your situation. Have you investigated all of your options beside foreclosure? Some include doing a short sale, bankruptcy and deed in lieu of foreclosure. If you do a short sale or declare bankruptcy your mom may get to stay in the house a while longer, check with an attorney.
Because so many people are going through this, you may find renting isn't as tough as you think. Each landlord will set the terms they are willing to accept regarding credit, but many are accepting people with foreclosures.