Is there a simple or cheap way to control Android Tv when I'm not at home? I work away and have found that the although she can't really use it my mother enjoys a lot of the content the box provides. If I could make sure she's got something to watch when she's not able to get out that'd be great.
Slingbox would be your best bet
If all you want to do is start stuff. Just set up a VPN to your home network and then cast to the device.
I use an app called Vysor with both a Vorke Z6 Plus and Nvidia Shield (NON-Rooted) and it works Great for both.. Mind you I dont go Directly to the boxes. I go to a Server, then use Vysor to get to the Android boxes. If you have a VPN it will work as well going directly to the box. Vysor is created by the Dev of Cyanogen mods as well. Its stable and works Great! Hope this helps.
Cheers
I stumbled across scrcpy at the weekend when trying to remote into my Shield on a local network and it gave me remote desktop functionality and was super easy to set up. Those instructions are windows specific but the main git for the project is here .
Performing the same from an external IP is probably possible - as it's an adb based solution - but beyond my capability at the moment.
For an easy, quick solution I'd probably run scrcpy on a local computer and remote into that using Teamviewer. In the absence of a local computer capable of running scrcpy, a raspberry pi running raspbian would do the job.