Hi. You don't describe how you are streaming video to Apple TV. You should try to use basic AirPlay if possible. Tje following describes the different AirPlay modes.
Video AirPlay works in two modes. Basic AirPlay just sends the video URL to Apple TV which then streams it directly. This usually works best since there's no double transmission. You're using basic AirPlay when the video player on your device goes black. On a computer, you do this using the AirPlay icon that appears in the controls of a screen video player object, in the browser or other app.
The other mode is Mirroring, which generates an H.264 video stream from the device frame buffer and transmits it over WiFi to Apple TV. This video compression inherently limits resolution, and may have trouble with fast motion. When you puit the iPad or iPhone video player into full screen mode, mirroring automoatically switches to basic AirPlay, and it seems to be impossible to prevent that from happening. On a Mac computer, you access this mode from the AirPlay icon in the main menu bar. It lets you mirror the main display, or create a new display, extending the desktop. But remember that the data sent to the Apple TV is always being converted to a live video stream. Actual display frame buffer pixels are not transmitted, as they are to a directly connected monitor.