Hello,
One of the possibilities for your symptoms is hand eczema. Wash the areas several times with fresh water. Do not use any cosmetic products at the sites. Your wife can apply some calamine lotion at the rash as it will help in soothing the skin. She can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate eczema a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid. Eczema can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
If the symptoms persist then please get it evaluated from a dermatologist. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Hi I suffer same condition and tried all the creams ( and loctite for splits ) best result was seaweed ! and what really got rid of it was uv photo treatment in Hospital. They said I had form of psorosis on my hands and in my case on feet also !