I was just researching the TPAPN website the other night for a friend of mine with bipolar, who's moving to Texas soon.
I've been on something of a soapbox lately about these monitoring programs, which are set up with the alcoholic/addicted/drug diverting nurse in mind and yet the mentally ill are treated the same. To my mind, it's punishing a nurse for having a psychiatric illness, as the programs are costly and force the nurse to take random observed urine drug tests, plus daily call-ins to an automated system that tracks them and penalizes them if they miss more than a day or two.
The nurse also has to be evaluated by their counselors and psychiatrists, also at her/his own expense. There may be stipulations placed on the license, such as no access to narcotics or part-time work only. And all this is for a minimum of two years, with five years being the usual term of monitoring.
Of course, you'll want opinions from Texas nurses more than mine; each individual state has its own way of doing things, and I know TX is stricter than most. That said, if your daughter wants to become a nurse, she should be able to, as long as her illness is well-managed. You can take a look around this site to find lots of bipolar nurses, myself included, who work and live as normal lives as possible in spite of our condition and the stigma that surrounds mental illness.
A lot depends on how severe your daughter's BP is and how well she adheres to her treatment; nursing school as you know is VERY stressful, and doing shift work in a high-stress job can be destabilizing. Knowing all that going in, she should be OK; however, she will almost certainly have to contend with the BON when she discloses her illness. It's possible that if she can produce evidence of long-term stability (e.g. letters from her psychiatrist and/or therapist, no hospitalizations etc.), they may not even make her go through TPAPN.
I wish your daughter the best of luck. Thanks for being such a good mom and advocate for her!