Your Dad is probably very allergic to nickel as I am. 316L stainless contains 10% - 14% nickel while the genuine 904L stainless Rolex uses contains 23% - 28% nickel so it would be even worse.
The allergic reaction is usually brought on by a combination of the heat and sweat. It seems strange how quickly the reaction is brought on. Perhaps try taking the bracelet off and cleaning it thoroughly with soap and water and then applying lots of clear nail polish. Afterwards, see if he can wear it a little at a time in a cool, dry environment and go from there.
Either way, it will most likely not be an issue after the weather cools off. Until then, there is always titanium =(
Good luck!