It still isn't completely settled as to what causes cholestatic pruritus but the best guess is that it involves conjugated bilirubin backflowing into the bloodstream. Bilirubin are blood cells that are old and dead that are floating around in the blood stream. Normally this bilirubin travels to the liver, is processed (conjugated), and then passes through the liver and out of the body through the colon. When liver bile doesn't flow, like with PSC, the conjugated bilirubin gets stuck in the liver and can flow back into the blood stream. The theory is that this conjugated bilirubin contains bile salts, etc. from hanging out in the liver and that this extra stuff can make a person itch when it hits the blood stream.
Itching hints of cholestasis. Imaging is warranted if it hasn't been done in awhile. If there are obvious strictures, a doctor may decide to conduct a therapeutic ERCP to open them up and help to alleviate symptoms.
The effectiveness for each therapy varies individual to individual. Experiment and see what works for your daughter. Therapies include:
1) Diet. This probably won't work alone but is worth a shot. My experience: my itching was exacerbated by dietary fat. A low fat diet helped to reduce cholangitis episodes and the associated itching (although a low fat diet is something I would not recommend long-term). Results will likely vary; try to cut out different things and see if it works.
2) UVB. Phototherapy can help to reduce itching (this is what they use in the hospital for jaundiced babies). UVB is what you are looking for. Good sources include the sun and devices you can get via prescription. Commercial tanning booths are primarily UVA and will likely be less effective.
3) Antihistamines. Benadryl doesn't do much for the itching but will knock you out and help with sleep. Over time your body will get used to it and it will lose its effectiveness. Atarax is a more hardcore version that is often prescribed. Downsides are extreme drowsiness.
4) Antidepressants (Zoloft). I'm not sure why these work but people have reported them useful for eliminating pruritus.
5) Cholestyramine (Prevalite, Questran). This binds to bile acids in your gut so that they are passed through the colon rather than being recycled. This means less bile acids getting in the blood stream via conjugated bilirubin so theoretically less itching. It seems to be a 50-50 shot as to whether it works (I didn't have any success). Downsides: It is slightly more palatable than colonoscopy prep and can disrupt a number of other drugs so a lot of caution needs to be taken regarding dosing schedule around other meds.
6) Rifampin. This is a tuberculosis antibiotic. I'm not sure why it works but anecdotally it seems to work better than anything else for directly targeting and eliminating itching. Doctors are reluctant to prescribe because it raises LFTs for a small percentage of patients.
7) Oral Vancomycin. This is a broad spectrum antibiotic that won't do anything to directly target itching but has been effective at eliminating the inflammation caused by PSC, in turn opening the bile ducts and eliminating itching. This was the solution that worked for me.