Good job on your sister saving the $10K. That's a great achievement. I think her challenge will be credit score. There are things she can do to get that higher and the higher it climbs, supposedly the better the rate she is offered. The book I just finished reading has a whole section on this topic (buying a house and low credit scores). I got access to it through the library and she might be able to as well. Have her check out - All Your Worth by Elizabeth Warren & Amelia Warren Tyagi.
She can do it! I know she can if she already saved up some money. Good luck to your family!