NOT A TEACHER
(1) This question always produces a lot of pleasant and courteous disagreements
(2) This is what some teachers say:
(a) Do you mind my marrying your daughter next month? = Is next month a good date
for us to get married? In other words, you are putting the emphasis on the "marrying."
(b) Do you mind me marrying your daughter? = Yes, I am poor now, but I will work hard
and make enough money to take care of your daughter. In other words, the emphasis
is on your acceptance of "me."
(3) As I said, some teachers say that it doesn't matter which one you choose. They
say that the context of the conversation will make clear exactly what the meaning is.
P.S. I love the "rule." I hope that you follow it, too.
Interested in Language