Untethered- sounds to me like there are two main issues here - 1. Concerns about the appropriateness and side effects of prescribed medication; and
2. How to ensure that you remain informed and/or your daughter is able to receive appropriate care where her best interests and well-being will be maintained.
I do not know a great deal about mood stabilisers except that they are routinely used with Bipolar Disorders and Schizo-Affective Disorder, and that side effects can also involve physical health issues, which need to be monitored closely, depending on the specific drug prescribed.
As it sounds like you are concerned about this and your daughter is still only young, I would suggest that you either sit in on a session with your daughter's doctor (with her consent) or otherwise request a "family meeting" with the doctor or treating team so you can discuss these issues and ask the questions that you believe to be important to obtain answers for. This may also be important for you in order to consider the reasons why this particular drug may have been prescribed over other alternatives (i.e. issues with compliance with oral medications where relevant, previous medical history, improved efficacy of a particular drug relative to other existing medications).
Otherwise, you may want to discuss these issues together with your daughter and write down a list of questions that she can ask the doctor herself.
It is understandable that you are concerned, although issues of patient confidentiality are always important. From my experience, you as an immediate family member would be crucial either as a carer or as a primary support for you daughter in the community and do have a right to be kept informed in order to ensure that she stays well and engaged with services.
When inpatient units have used the old line about confidentiality with me regarding my family member to withhold important information, I have found that when I make it clear to them that she is severely impaired (which is already obvious) and that I am most likely going to be the person left responsible for her care and support upon discharge, AND that I am seeking to ensure her best interests, they usually relent to a degree and will be willing to discuss issues that are important regarding her treatment and recovery.
In outpatient and community settings, this may not be as clear to professionals. Due to her age, they may possibly be concerned about supporting her capacity to establish her own independence and make informed decisions regarding her treatment. It is important where possible to try and establish a positive partnership with your daughter's care providers and maintain an open, trusting relationship with your daughter in order that you will know the signs that she is not doing well and when she requires further help, and to know how you can best support her.