They make what you want but not for the price. Does the vehicle you are buying have a back up camera? If so, the should help with hooking up the trailer. As for being on the back of your trailer, that's a different animal. They have wireless and wired units. If tied to a screen in the car then you can't use it while driving without a hack or product that allows the screen to be used while driving. Otherwise a separate screen is necessary. You might look at aftermarket stereo's with screens. Many offer options that use a camera mounted on the license plate frame.
But for $100? Good Luck.
Let us know if you find something. If you do, I would also be interested in adding one to my trailer.
