RE: travel trailer rental
The problem with being in a trailer, unless you're in a campground with full hookups, is going to be waste water storage capacity and electricity. A small camper is going to have small holding tanks. Our family of 3 taking very conservative showers, washing dishes, etc can easily fill our 40gal grey water tank in 4 days. You've gotta be able to shower when you're hunting so I can see this being a problem. Also, without hookups, you'll be running all of the lights,etc on battery power. Two batteries will get you thru maybe 4-5 days if you are really careful.
Either way, without hookups you will run out space and power long before a week of hunting is up. If you are not boondocking and are in a campground with full water, electric and sewer hookups there should be no problems. You won't save anything on gas by towing it from Ky, so unless you can rent it in Ks I wouldn't bother.
Good luck!
Shaun