i am going on a cat hunt in idaho and i am flying from the east coast, what is the best way to bring my hide back?

I'd contact a few taxidermist near the location that you'll be hunting, and plan on having them do the taxidermist work, unless you're having a full mount done. Even if you're planning on having a full mount done, a local taxidermist can prepare the hide for the mount and then ship it to your taxidermist. That would be easier than shipping a raw hide. If you can get the raw hide frozen, and keep it frozen, then shipping the raw hide would work too.

i ll be able to freeze it but didnt know about taking it on the air plane

Ya you can either flesh it out and salt it and put it in a garbage bag, then when you get home let it breath and re-salt. or freeze it and put it in a cooler with dry ice.

Just buy her a ticket. I think strip clubs and brothels are legal (or at least overlooked) there. If you just get the "lady" a ticket, nobody will even know the difference about what she does for aliving.

Depending on flight time, flying it back might be an option. What would it weigh? Under 50 lbs? Depending on luggage rules and flight times, you could possibly freeze it, stick it in a cooler from out there and fly it back as extra luggage...if there is spare room in there, you could even buy some dry ice to put in there.