Podmog how awful!
Have you heard of using Aloe Vera Gel, soap, bath gel, shampoo, and conditioner - all sorts in fact! from a company called Forever Living Products, you can also take the drink which is proven to relieve the itchiness remarkably. They have a website full of information regarding skin conditions... www.foreverliving.com
I am a distributor but I am not trying to sell you anything! - check out their website, find a distributor in your area, and organise for a sample to be sent to your home. They have a 90 day money back guarantee no matter how much of the product you have used! So do try it, and it may help with your child's hands.
Good luck and let me know how you get on!