As I see it, there are two problems here. First, as other answers have indicated, "no credit" is not looked upon favorably by Conventional Lenders. They feel they are dealing with an "unknown" quantity. The second problem is the amount of the loan. Most Banks and Mortgage Lenders do not want to deal with loans that small. As I understand it, $50,000 is the very least they will even consider.
There may be Private Lenders that are Licensed in Texas who can help her. They well usually lend for 10 to 12 years. Their down payment will probably run 20% to 30% and their interest rates will be higher than Conventonal Financing.
The other option would be "Hard Money Lenders". These are lenders that are usually used by investors but in this case, they may be what you mother could take advantage of. Their terms are pretty much the same, except they lend for shorter periods of time. Many will only lend for 12 to 18 months but some will go up to 3 years. Those are the ones that you need to find.
In 2 to 3 years, your mother can establish her credit and qualify for a much less expensive Conventional Mortgage. One such company that I have dealt with and had good results isThe Westmoore Group. The will finance up to 3 years and do not include any kind of pre-payment penalty clause in their contracts Unfortunately, they are licensed only in Georgia and not in Texas for longer term Home Mortgage Loans but deal Nation wide in Hard Money. But due to the fact that they will lend up to 3 years, they may be of help for your mother. Here's their contact information if you would like to speak with them to see if there is any way they can help you.
The Westmoore Group, LLC
Ph: (646) 801-6190
Fx: (646) 619-4291
The Westmoore Group, LLC is a licensed lender in the State of Georgia and operates under the license #30544.
Best of luck in getting her financed and into a new home.