I am so sorry to hear about your little girl, it must be horrible for her to understand and deal with. I have a little girl who is nearly 2 and I know if she was afflicted it would be terribly traumatic to have to watch her suffer.
I am from the UK too and have been recently diagnosed with LS aged 33, luckily I had a great doctor (and private health insurance!) and I didn't suffer very long before being diagnosed properly.
I was prescribed dermovate by a very knowledgeable dermatologist and she said it worked wonders. I will keep it for if I ever get desperate but I would rather get to the bottom of why I got it in the first place and try and find a natural cure.
I too have resorted to Emu Oil, I have used it for 1 week and the LS is very nearly gone. I am going to try DMSO too, it is derived from wood bark and works by drawing oxygen to the area. You may have to get these things from America, my sister sends them to me from Australia.
I have been to a very good naturopath in Manchester (let me know if you live near and I will send his details). I had a food intolerence test which was very useful. I now avoid all wheat and cows milk products (I have goats milk, goats butter and goats yogurt). It wouldn't surprise me if most people with skin disorders had an allergy to cow's milk and I would certainly recommend she tries to avoid it, along with sugars which tend to aggravate it by 'feeding' skin disorders. Try and keep her diet as natural as possible. I have done lots of other things but nothing I would recommend for a little girl (like a parasite cleanse and a colon cleanse) and I feel a million times better than I did a couple of months ago. I think my LS was brought on by Adrenal Fatigue caused by working my socks for years, LS just seemed to be one of the many illnesses I got over the past few months and it was the last straw - no more working my fingers to the bone for me.
I hope the poor poppet does get better soon and let me know if I can help you with any more information x