Rifles on plane are fine, check with TSA AND your airline for their rules. I know for afact it must be a hard sided case locked and unable to be opened without unlocking. Ammo must be in its original container or a container that protects the primers (magazines are unacceptable). There is a limit to how many rounds can be in the case with the gun but they can be tossed into checked luggage no problem.
Most hotels require you to check them with security, but DADT, if your using a pelican case whos to say its not camera equipment? Keep it locked up in the room (obviously). For hunting the area i leave that up to others, im still new to the scene and hoping to make this a good season for me come sept 1 when the pups are out the den.