One thing I've found that will really help those dry cracked hands is to apply a good quality hand lotion before I do any household cleaning chores, but especially before I hand wash dishes.
Just apply your favorite quality hand lotion as normal. Rub in a generous amount.
Next, slide on a pair of rubber gloves (or regular latex gloves if it's all you have) before you begin to wash dishes.
The heat from the dish water will heat up the hand lotion causing it to be more easily absorbed. The rubber gloves will hold in moisture while your hands get the TLC they desire, all while keeping out hard detergents and the affects of the hot water.
Give it a try. You'll see the difference right away!
Only By His Grace,