I too have a Phantom, only Vision Plus. My controller emits a wifi signal that connects to the drone's camera and to my IPhone and it is through the IPhone that I get the FPV, no internet necessary. I think your drone works very similarly to mine, so internet on the phone, or 3G or 4G signal will not be an issue. I had good satellite connectivity everywhere I flew,m which was in Santo Domingo and Las Terrenas.
I flew JetBlue and like you I was concerned about bringing the batteries on the plane. I did not have any issues. I bought a foam backpack specifically for the drone and brought it on as a carry on. It does seem to me that if one of those batteries exploded mid flight and ignited a bag, or something, it could be disastrous. A plume of toxic smoke would quickly fill the cabin and I don't know if the air handlers on the A-380, or whatever, are good enough to clear out that kind of smoke... I think hard fire proof carrying cases for such batteries is a reasonable regulation but as far as I know, there is no such regulation or requirement.
I was vaguely aware of the IDAC regulations. But I figured there are countless laws and regulations in the DR that are not enforced, drone regulation is pretty far down the list.
PM me if you would like the link to a video I made, including drone shots and non-drone shots!
Good Luck!