re:
There MAY be a way to accomplish this, BUT it's not built in to the design of the device. It is however possible you can find a system that transmits a signal from the device's output to another location in the house. The negative of such a system is that both TVs would have to watch the same thing, plus this type equipment is not cheap. You would need something LIKE this...
https://www.amazon.com/Sling-Media-...ag=hawk-future-20&ascsubtag=UUimUvbUpU2878901
NOT THIS, though it's for the Slingbox, but it's the principle you mean. It's no longer made, but they probably have similar products you can find. Now here is my question for you. WHY paid for an elaborate setup for sharing an Apple TV, why not just buy a second one? Apple has a refurbished store that DOES have them (my refurbished 3rd gen has served me well for a couple years now!), a 32GB 4th Gen is only 129!
PS Another good option is you don't mind going off the Apple reservation would be the Amazon FireTV stick which you can get for 39 dollars (sometimes cheaper on sale) at Amazon.....
https://www.amazon.com/All-New-Fire...ag=hawk-future-20&ascsubtag=UUimUvbUpU2878901