I can tell you how it worked last year when we came back from Little Cayman but I am not sure about the trip down because we vacationed on Grand Cayman before going to LC.
Coming back was not great because we couldn't get a direct flight on Cayman Air from LC to GC. So we had to check in at the LC airport, fly the Otter for about 5 minutes and land on Cayman Brac, reclaim our luggage and go through security and check in on Brac, fly the turboprop to GC, claim our bags, go outside and then come back inside the main terminal to check in on AA for our return flight. Then go through security, customs, immigration in Grand Cayman.
We could not get a direct flight to Chicago from GC because we were traveling during the low season, so we had to fly to Miami, collect our luggage, and go through US customs and immigration to enter the US. When we finally got to O'Hare we handled our bags for the 5th and final time and went home. In all, it took us 12 hours of travel time and we visited 5 airports and traveled on 4 airplanes just to go 1600 miles - kind of ridiculous but it was the best options we could find.
When we traveled from Grand Cayman to Little Cayman we were able to get a direct flight on the Otter and didn't have to stop on Brac, but we couldn't get a direct flight coming back.
We booked our trip more than 7 months in advance but we also couldn't get a flight back from LC on a Saturday so we had to stay an extra night on LC (not a hardship!) to fly home on Sunday.
We were staying at the Little Cayman Beach Resort and they offered a nice option. You can pack and check one or two bags the day before you leave and they will pick them up and send them to GCM so they are waiting when you arrive. It was a bit of a rush because we did the 2 morning dives on our last dive day; spread out gear out on the deck to dry as much as possible while we ate lunch, and then packed it to be picked up by 2 pm. But it was nice not to have to deal with the gear as we traveled from LC to CB to GC.
Have fun on your trip!