It's not complicated, it's just not intuitive.
1) Open the app
2) Make it start streaming
3) Make it full screen
4) Swipe up from the bottom of the screen (this is the part she never remembers)
5) Activate AirPlay and select the right device (in my house they are Apple TVs so they have good names, but if it were in every TV, they would have strange names
5b) If you've never streamed to this TV before, put in the auth code
At this point it will play to the TV. However, since I have an older iPad, it plays a 16:9 image in a 4:3 box on a 16:9 TV, so it doesn't use the whole screen. So then you have to go to the TV and change it to "zoom" mode to use the whole screen, which of course isn't at full resolution at that point.