I haven't found the family in the West Indies yet, but at least we can fill in a little more info for Carroll's wife. She was Catherine - not Kathleen - per census:
1940 CENSUS New York, New York, New York, USA 161 Manhattan Avenue Carroll Watkins 45, born British West Indies, Naturalized, exterminator Catherine 46, wife, born Irish Free State, Naturalized Carroll 21, son, born New York, attendant, law association John 18, son, born New York 1935: they lived in the same house
She seems to be called "Ketty" in an earlier census. An Ancestry.com family tree has her as Catherine M. “Kitty” Watkins born 20 October 1893, Irish Free State - CAUTION this needs to be checked, don't take it as fact.