A couple of thoughts.
I would be thankful to be related to a doctor if my sibling wanted me to address them as Doctor. The reason I would be thankful is because I would surely need a medic to help me repair what I busted from laughing so hard at the request.
As for the Caddy comment, maybe since you are very concerned that they address your DH as Doctor you possibly come off as not so nice so that is why they made the comment and rolled their eyes? I don't know and I don't know you so I am not saying whether you are nice or not but from this question I wonder if you might come off as a bit high brow if you will.
Oh- and I don't make an appointment with my sibling to visit nor do I come bearing gifts everytime I see them. Of course I talk to my sibling every day.
Obviously you have a pre-existing bias here, because at no time did I ever make a request and I made it clear in the OP that I would never mention it.
It could also be a "generational thing". I address anyone older than me by Mr. or Mrs. unless I am asked specifically to use their first names. I addressed my aunts and uncles by the title, "Auntie and Uncle", and I expect the same in return. If my friends and neighbors heard the term "high brow" in relation to me, they would laugh. My favorite shoes are flip flops and that is what I wear when I am not mowing the lawn. Unlike my SIL, I do not have a Coach bag, not that there is anything wrong with that, but tend to stick to my LL Bean canvas"healthy bag" unless I get really dressed up.