Don't give up on finding a new T & pdoc, also new meds they suggest.
Read "everything" you can get your hands on about psych meds for teens, as some of them are the same for adults. Learn everything you can about her previous dx & what you think her symptoms are based on your observations are & what she tells you.
Are there any outpatient (day) programs that have a good reputation in your area? Before she goes inpatient visit first if they will let you. Check their reputation, google, whatever you can find out, what kind of patients they treat?
With this particular school she's in now, if she skipped a year would they let her back in the next year? Since she's failing now, it will affect GPA.
A lot to consider, like you wrote in your post. Sometimes "you" have to make these decisions, 16yr olds are not adults yet no matter how mature they are or seem to be.
I could go on & on I suppose.
Am bioplar myself & raised a bipolar son. Feel free to PM me anytime.

Best wishes for all of you.