Well the first step in solving any problem is to define the problem. I know, you see the problem as your friend is potentially being sent to a Wilderness program. But one question is ?Why??. Her mother must feel there is a problem, try to find out what specifically the mother feels the problem with her daughter is (acting out, drugs, sex, grades etc.).
Once you have defined the problem you need to convince her mother that Wilderness is not a good solution (as you believe it is not) or provide other solutions which involve not being sent away.
If the problem is drugs, for example, you may try to provide evidence to her mother that wilderness may not be effective for this. People here at fornits can help you with some of the wording.
I would not waste time trying to convince her mother she doesn?t have a problem, initially, because she has already networked with other parents and the problem is real to her. Avoid threats, running away, acting out more etc. this will only make it worse for her. Keep it mature and focus only her choice of solution (Wilderness Program).
Hope this helps and things work out for you and your friend.