The natural reaction of modern society is to add a topic ointment, pill or remedy to a problem. In some cases this can work, but, it often like playing the lotto.
Holistically, one has to try understand the root cause of the problem. Very often there is a 'trigger' involved, which, has caused this to happen. No amount of 'add-ons' will take away the trigger.
The fist things to look at is diet. I had a girlfriend with Alopecia and my sister has cradle cap. Both of these sinister conditions seem to be irritated by underlying food allergies.
Eczema is another skin condition which often falls under the same umbrella.
Remove all hyper-allergenic foods from her diet for 30 days and watch for a difference. Wheat happened to be the one which exacerbated my sisters symptoms the most.
Here is a comprehensive list of most allergenic foods:
https://www.fda.gov/Food/ResourcesForYou/Consumers/ucm079311.htm
The other causes can range from stress to irritants. I doubt a girl of her age suffers from anxiety. The other thing to look at is her current shampoos. Try look for sulfate free variations, or, use a Johnson & Johnsons baby shampoo for a while. The milder the products, the better.
I really hope you guys figure it out. Let us know what happens
Wow, your detailed response is massively appreciated.
I resonate with the idea that there is always an underlying cause. Though it's tricky to isolate the issue here.
Her diet is very similar to the one her brother had and he didn't have the condition.
I will check out the list you provided.
It's a pleasure. I feel for your daughter, as I know how my sister suffered from the condition.
The none invasive nature of the above recommendations make them attractive to try out.
I would never generalise when it comes to genetics. Despite having the same parents, your kids will vary in many of their traits and gene expressions. Every human being needs to be seen as genetically unique.