My wife is suffering from her dry hands. we don't know if this is caused by detergents. tried to use gloves but it worsens. she has cracked skins.

Allergy testing: She may also be allergic to a substance used in the gloves (ie: latex) which is why the gloves may be causing her to worsen. There can be many causes including chemicals, soaps, detergents, materials. She should see a dermatologist for patch test and an allergist for allergy testing. In the meanwhile try aquaphor or vaseline to help with the dry hands.