The Comfort Suites is generally a good choice for a short stay on GC; you are easy walking distance to restaurants and bars - but hopefully you won't need to got there because you will want to start your Cayman Brac vacation without delays!
The flights to Little Cayman are tighter than Brac because the LC airport is small and only accepts little planes and it doesn't have lights - so you can only fly in and out of LC during daylight. But Cayman Brac has a larger (lighted) airport and they accept jets, turboprops, as well as smaller propeller planes - plus they serve as a connection point to flights elsewhere in the Caribbean; so there is a good chance that they will get there the same day.
What day of the week and time are you flying into GC? When you arrive on GC, there are sometimes long lines to get through customs and immigration - and then you have to claim and recheck your bags for CB, and go through GCM security to get to the departure lounge to board your flight to CB. So 45 minutes does seem like an awfully tight layover and you could miss your flight to CB - hopefully there will be later flights to CB that you can catch.
Here's another option, I have not tried this but there are "Meet and Greet" services available on GC (see the links below) that will ease your passage and make sure that you make your connections on time,
@Testudo may be able to give you more information because he is a local.
Meet and Greet Service – CEO’s Welcome
Businesses on the island are not always promptly responsive to emails, so if you don't get a response try calling them at +1 (345) 943-7070
Here's another service but they may be more expensive:
Royal Airport Concierge