There are some skin conditions associated with cancer that manifest as sores on the body, like Kaposi's sarcoma. The fact that he didn't want her in the room seems kind of telling. (Do you know for sure that he doesn't have HIV or AIDS?)
But there are a lot of reasons a serious alcoholic might have sores on his body, and it's impossible to diagnose on the Internet. All you can do is ask your mom to ask his doctor, and if the doc won't tell, she should work on your dad.
I think if my alcoholic husband refused to have me (his wife) privy to the information regarding sores on his body, i would first get myself tested for all std's and refrain from fluid contact until having done so. It is highly suspect that the husband will not allow his life partner to know the results.
What i found on skin sores due to alcoholism is the following. " Skin, Muscle, and Bone Disorders
Severe alcoholism is associated with osteoporosis (loss of bone density), muscular deterioration, skin sores, and itching. Alcohol-dependent women seem to face a higher risk than men for damage to muscles, including muscles of the heart, from the toxic effects of alcohol."