If the U.K. government asked us to send in the Marines, I'm sure we would within hours. But they haven't. Instead, the Brits have sent some naval personnel in to try to calm things. That may be inadequate, but it's Tony Blair's decision. The last thing we'd want to do is show up our ally.
I'm assuming there's no right to bear arms in the Caymans? Times like this is when that right is needed the most.
One option would be to dispatch a couple of Coast Guard cutters with some Tactical Law Enforcement Teams on board. This is a "humanitarian" situation and the existing agreement with the Grand Caymans and the Coast Guard would work.
I'm sure there's no RKBA in Cayman, so when the power goes out, machete wielding gangs are the only power. Glad I live where at least I can defend myself.