If you connect a second AppleTV to the second TV set, you can watch whatever you want on it. They are independent devices although can be tied to the same iTunes Store account for purchases and rentals.
You'd also have to check that your internet connection is fast enough to support streaming to both devices at the same time.
Bear in mind though that AppleTV is a streaming service - it doesn't receive broadcast TV programmes like Sky does. You don't tune-in to specific channels to watch specific programmes. Everything is on-demand (except for the occasional Apple special event which is streamed live).