I remember there an app that controlled appletv mouse n had keyboard on iPad app that used for input
I thought it was remote but not sure which app
Advice
"Remote", which is a free app from Apple does indeed act as a remote for AppleTV. the keyboard only shows up where appropriate - like when you go to a search screen. There's really no mouse - swiping emulates the up/down/left/right keys on the remote, not cursor control.
Search the App store for either Apple or Remote and you should find the app.