Thanks for the question: it is an interesting one. There are certainly many many examples of yoga being a valuable tool in psychotherapy. Amy Weintraub, as one example, has written a whole book on Yoga For Depression. Bija Bennett has written a book called Emotional Yoga: How the Body can Heal the Mind. Outside of the pure, physical yoga, the book The Mindful Way Through Depression is very highly ranked on the Amazon.com booklist. Inside YinSights, you can also find several chapters dealing with the mind and Cognitive Behavioral Therapy (see
http://www.yinyoga.com/ys1_4.4.2.0_cogn ... herapy.php)
Generally, most authors and researchers I have read won't claim that yoga alone is a cure for addiction, depression or other psychological problems, but yoga can be a powerful assistance in dealing with these issues. One of the first benefits is due to yoga's ability to allow people to relax and drop their stress. It is very difficult to heal when you are distracted and uptight. Fear, anxiety and repressed anger can get in the way of change. Yoga allows people to let go of their fear and anger. Many people are also quite disconnected from their bodies: yoga helps to bring them back inside, which is where the changes have to occur.
Another big benefit for yoga in dealing with clients/students who have psychological challenges is that yoga will help them regain their physical health and stamina. A healthy body does lead to a healthy mind. Or said in reverse, it is very difficult to have a healthy mind if the body is ill or weak. Obviously, not all forms of yoga are going to work for every body. An extreme Hot Yoga or Ashtanga practice may not be the best form of physical yoga for students dealing with emotional challenges. A quieter, more restorative or internally focused practice, which Yin Yoga is excellent example of, may be the preferred initial practice. Sarah Powers' new book, Insight Yoga, may also offer assistance through her description of practices that combine inner awareness with the healing energetic benefits found in Yin Yoga.
If you are looking for specific suggestions - these are tricky. Every person is different and requires different "medicine". A severely depressed person may indeed do better with a more lively, active Yang practice, or perhaps some simpler moving flows such as the mini-sun salutations (see
http://www.yinyoga.com/ys2_2.2.7.1.2_mi ... tation.php ) or the cloud salutations (see
http://www.yinyoga.com/ys2_2.2.7.1.3_cl ... tation.php). Other students with anger issues may want to do the Yin Yoga practices that target the Liver/Gall bladder meridians (see
http://www.yinyoga.com/ys2_2.2.6.5_flow_for_liver.php ). Others, who may be dealing with fear and anxiety may find more benefit in working with the Kidney meridians (see
http://www.yinyoga.com/ys2_2.2.6.4_flow_for_kidneys.php ). For those with cognitive or behavioral issues (such as addiction), you may want to do some guided reframing work while they are in a deeply open state during the long Yin Yoga poses.
I don't believe there is one practice that is right, or even safe, for every body. As the therapist/teacher, you will have to combine your specific knowledge of the individual you are helping with your wide base of knowledge of the yoga toolkit, and then decide/tailor the practice for her.
Cheers
Bernie