I have to say, being disrespectful to authority figures and hanging out with kids that you don't like is not "pathology" its a choice or personality.Therefore, you are looking to wilderness not for treatment of sickness but as cosmetic brain surgery.
Its not fair to try to wipe out elements of a personality you don’t like. You’re not creating your ultimate buddy. You want to let her develop a healthy, human, and individual brain, not one custom tailored to your desires. Babies can be fidgety, young adults and adults may be ornery.
Further, Perception of those characteristics is a subjective. There is no "disrespectful" or "undesirable peer" measurement system that has scientific accuracy, as there is one for cancer or asbestos.
The perception of those characteristics may be inaccurate. Further, those characteristics may be reactionary to disrespect she is receiving at home. To wit, they might not be "problems" but reactions to problems.
I don’t know if you are a real person or a fake. But sending anyone, for any reason, on a forced march is not therapeutic. The Jews went on a forced march. The Native Americans went on a forced march. Neither group was much fond of it nor would they relate it as a "healing" experience. It is, in fact, traumatizing, potentially deadly ,or permanently injurious experience of abduction, false imprisonment, slavery, and finding out first hand what it is to be reduced to a steer. It is an Orwellian nightmare. Having your own mother do this is an Orwellian nightmare meets "flowers in the attic" maternal betrayal. It causes alienation from society, the family, the self and mental damage. Kudos to the Nazis and the Americans, for lacking the perversity to call this violation "therapeutic" and charging their respective victims' families for the "help"
You are creating a personalized Trail Of Tears for a 13 year old girl.
You don’t have to be a genius to figure out that WP is snake oil.
There have been NO studies that show this does anything other than HURT young people placed in them.
Think about it for yourself, you are abducted by some goons who "force" you to hike for ....months? 6 months? How do you think the "forcing" is done? Its through
1)physical violence, both by staff, who have nothing more than high school diplomas-if that and other kids forced into this program.
.2)FOOD DENIAL.
3) Forced exercise in addition to the march
4) Deprivation of equipment like blankets or tents,
5) Forced public nudity,
6) Group violence ,physical and emotional. IE. "Jane" wont march everyone do an extra thirty jumping jacks. Now tell her what you think of her". Now show her what you think of her. Your daughter will literally be dragged up a mountain by other children if it came to that. Your daughter will be the victim of violent crime
7) Staff emotional abuse IE "Jane why are you such an ugly hoar?" You can count on the staff making fun of her body at some point while she's there.

Isolation
9) Denial of water or clean water
These are just some highlights. It wouldnt be OK for u and it wouldnt be Ok for her
Also, all wilderness has a strip search component upon entering which would be especially damaging to a girl who has body issues.. These are just some highlights.
As an anorexic this is especially dangerous for her physically as her body is weakened and physiologically unbalanced and brittle. Her body can only be injured by this experince. Strenuous exercise where she is not allowed to stop participating if she gets tired could quite easily kill her. It’s killed perfectly healthy kids in large numbers. And if they do kill her, they will BLAME you for putting her on this trip with a "pre-existing" condition
Her death will be referred to as part of the "window of loss"
If any "professional" recommended wilderness for her, I suggest you find a lawyer and sue for endangerment. I’ve never heard of anything so irresponsible!