If my bank revealed my checking account balance to my mother but the account is in my name only, what recourse do I have?

Every bank is required to have certain policies in place to insure the privacy of the information relating to their customers.  If they breach that duty, then you could potentially file a tort/invasion of privacy suit for unauthorized disclosure of the account information.  A consumer law attorney will have the best skill set to help you with this type of claim.

If you don't want to go through the hassle of filing a lawsuit, but instead just want to send a message to the bank of "be more careful," you can simply file a complaint with the Texas Department of Banking through their website at:  http://www.dob.texas.gov/dss/ccmain.htm