Thank you ma'am
I am sorry for this dilemma. The sad truth is that she has no right to demand a retest of the urine. Even had she gone into the service, there is no right to demand a retest.
So they can discharge
Now the good news (if there is any good news) is that she will not get a "bad discharge". Since she never went onto active duty, they will give her what is called an "ELS" or entry level separation
This is a separation that is not characterized. So she does not have a "bad" discharge.
If the discharge was approved then she is out. There is not anything she can effectively do at this point.
I wish I had better news.
This lack of due process (her lack of ability to fight this) is tied directly to her status. Because she had not formally entered the military (by going to bootcamp) she has very little in the way of due process rights. Other than requesting that they reconsider their decision, she has little in the way of recourse.
Now...can she join another service?
That will be up to the service. This separation will show up on her record. SO other services will know about it. But it is still possible, at least in theory, for her to join another....it just makes it a bit more difficult. She would need to obtain a "waiver" or specific permission to enter despite the prior separation. The waiver would be decided by the recruiting command.
The largest problem she will face is the economy. The poor economy has sent kids flocking to the military for jobs...because of this the military is not giving out waivers very often.
That can change...if the wars get worse or the economy improves, the military will need to provide more waivers. So there may be an option in the future to allow your daughter to enlist.