Not sure why you posted this in "The Lighter Side"?

Joseph Carter is a very common name - even Joseph T Carter isn't exactly rare?!
Have you found him on the 1939 National Register?
I looked at FreeBMD for a birth for Florence (as the least common name of the 3 children). But there are so many Florence Carter's out there!
Between 12 and 20 every year!
I'm not sure your family tale really holds water?
How did a "Scottish Granny" still manage to produce 3 children?