In my opinion you're definitely overthinking it. The written consent to take your girls out of the country might be needed to leave the US but immigration in Jamaica will probably not even ask anything about it. Your purpose is a vacation. You don't need to say anything more than that if you have a return flight booked and your intent is to return to the US. If you are staying longer than the allocated time then you might disclose more. Earlier this month everything was done online and then at a kiosk. Then I stood in the nothing to declare line and was passed right through. The online form will ask where you're staying. If it isn't a listed hotel on their online form then they may ask you where. You do need to have an established address of where you're staying. One of my brothers met me down there one time and didn't know exactly where we were staying because I booked the hotel and was picking him up at the airport. By him being honest and saying he didn't know what hotel he was staying at and that I was picking him up they gave him some problems but eventually let him out to the arrival area to find me and get the hotel info.