Some campgrounds convert the digital cable signal from their cable or satellite provider into an analog signal and pass that along to the hookups in the campground. Some campgrounds just put the digital signal through but without the need for a cable company specific receiver (the box the cable company rents to you to connect to your TV set at home to the cable line whether a digital or analog TV set).
From what you describe Disney is putting a digital signal through and they lent you to use a digital to analog receiver box (sold in most electronic stores) that allows an analog TV to receive digital signals and display them. This box that they gave you is no different from the digital tuner that you will have built in on a new digital flat screen TV sold now. The trouble that you had with this box must have been the result of a poorly working converter box, a cheap converter box, or one that has been passed around so many times that it has been damaged along the way.
If you are not going back to Disney any time soon you have time to shop for a flat screen, digital TV for your RV. You will find this TV everywhere that sells TVs. They will be 110 volts - if you want a 12 volt TV you can get that too but will have to look where RV accessories or marine accessories are sold. Any TV that you pick from those available today will work. You will have to scan for channels with the TV every time you hook up to cable or with the antenna in a new place for the first time. You should also have had to scan with the box Disney lent you - without scanning you will not lock in signals. No campground really tells you about this regarding TV and cable as the process is pretty much standard now for RVs with newer TVs.