My mother is looking to take out a loan from her 401k, approx 12K. I will be purchasing a home that she will be living in. She doesn't have good credit so the mortgage will be in my name and my sisters name. Her 12K would be put to help with the down payment. Her
401K is asking her why she wants the money. Will they give it to her if she basically says she is giving me the money? Does she have to have proof as to where her own money is going...

Depends on the rules of her specific plan. Some plans allow employees to take loans for whatever purpose they desire; others limit loans to specific purposes such as the "hardship" cases as mandated by the IRS. The plan administrator should be able to let he know what the specific rules are.