Two hours should be enough time even during the busy Christmas week. The only snag might be if your flight(s) from the US are delayed and you arrive on GC late. If that happens, try to grab the attention of an airport employee in the Customs and Immigration area and tell him/her that you are in-transit and traveling on to Cayman Brac and that you are in danger of missing your flight on Cayman Airlines to Brac. They should bump you up in the line.
If you can't flag down an employee in C&I, you might try going straight to the resident's line - which is usually shorter and quicker - and explaining your situation to them and asking for help.
After you get through C&I you have to go to the Cayman Air ticketing desk to check in and recheck luggage. That used to be a bit problematic but now it is much easier with the new airport - it's all indoors and not very far away now, and you will find free luggage carts in C&I that you can use - unless they are all snatched up quickly during Christmas week - try to snag a cart.
If you get to ticketing lounge and find that there are long lines at CA, look for the automated kiosks you can use to check in and check luggage. You could also grab a skycap and tell him of your situation and he may be able to bump you up in line. Be sure to tip him well!
If you are bringing any duty-free liquor in with you, purchased at the last airport before you leave the US, remember to pack it carefully inside your checked luggage before re-checking, because you will have to go through Security and you cannot take large volume liquids through Security. Amazon sells some re-usable padded bags for alcohol.
The Security Lines usually move pretty fast in the new airport because they have added more lanes and staff, but again, if you are running against the clock, speak up and ask for help. Things get hectic on Saturdays between around 12 pm and 3 pm and especially during the busy season.
Have a great trip!