My mother took out a payday loan that went into default over a year ago the payday loan company has drafted these funds out of another account at a different financial institution that she did not even have when she originally applied for the loan. Is this legal in the state of Texas? I read in the state of Texas an "ordinary" creditor other than the fed gov't or court ordered child support cannot attach or garnish accounts.

You may want to have your mom go back and read through the paperwork that they give to you when you take out one of those loans. If it states in those documents that she signed that if she defaults they can draft any other accounts or assets that she may have, I believe they are acting well within their rights.