If you are having mouse/touch input issues on your screen that's normal, some games use up all the input and doesn't let aurora have it's own.
First, make sure it is indeed the game messing with the input by going to your controller layout and change the right and/or left trackpad to mouse and the trackpad press to left and right click. Go back to aurora then check and see if still doesn't work. If it still doesn't, then you will have to go to desktop mode since there is no solution for gaming mode currently. In desktop mode you should be able to switch between windows by pressing alt+tab (if you don't have a keyboard set your back button to right alt+tab, it must be right alt since the left alt wont work, and set tab as sub command), switch to the aurora window and if there still is no input then your game's fullscreen is interfering, switch to windowed mode by going to settings or by clicking alt+enter, or by typing -windowed on the games launch settings.
Other notes
-Make sure steam overlay is disabled, and enable developer mode.
-On gaming mode, typing "-windowed, -borderless, -sw, etc" as launch commands used to work from what I read but not anymore.