I have dealt with dry hands and splitting skin at the edge of my finger nails.... My Dad had this issue.
I finally broke down and went to a dermatologist, a real Doctor. Of all things she had this condition, also. She had done extensive research. She explained to me that it was a genetic condition. At one time my Dad was told the same thing by a Doctor. So, part of the reason comes from the gene pool.
Second, she explained that IF I could remove all of the "perfumes" from all of the products I use, that would help the condition. Things like Downey fabric softener, certain clothes washing detergents are highly perfumes (Tide, etc), use a different soap to wash dishes. I got away from Dawhn dish washing soap and moved to some that were not as harsh. Shampoo was also a place we pick up perfumes so I went to a less scented shampoo..... The list of perfumes is long and, as she agreed, we will never remove all of the perfumes but we can eliminate the majority. Just make notes on anything that can be absorbed through your skin.
Next, I upped my vitamin intake... Rather than take a multi vitamin, I started taking specific vitamins and nutrients. American's are consuming large amounts of processed foods and we are shorting ourselves on basic vitamins. I jokingly tell people I am on vitamin A,B,C,D,E and if there were more lettered vitamins I'd be taking them.
My "go to" hand cream is Aquaphor Healing treatment. I slather that stuff on my finger tips and put on a pair of the cheap blue gloves from Harbor Freight and then put on my regular work gloves.... At times when the condition gets real bad, I will wear the blue gloves to bed to hold the Aquaphor in place on my hands...
In my case, wearing wet / damp gloves compounds the issue of finger skin splitting... Being in Montana, the weather condition certainly is a challenge.
I have tried all of the above mentioned products with limited success... In my case I can literately feel pain in the area that is going to split a day before it actually starts to split and I double up on the remedies.
The road to healing your hands is a long one that requires due diligence in maintaining them.
Finding a Dermatologist that really understands the condition is difficult... Like a needle in a hay stack.
Best of luck...