Make it harder to escape
Maybe you could make it so you have to hold down the escape/exit game button for several seconds instead of working with just a tap.
Karen MacDonald commented
I use the iPad's Guided Access feature to block out the area of the screen with the 'get-out' button, so they are forced to stay in the programmed games. I am always nearby, so if there is a genuine need to get out, I can do so, but they can't just quit if they are a little frustrated.
To activate Guided Access for the first time, go into the iPad settings, select General, Accessibility, and switch Guided Access to On
Guided Access is then activated in app with a triple click, then you can highlight whichever part of the screen you want inactivated (useful for banner ads too), then activate. You triple click to get out again, with a passcode. It can also disable the home button, so stops them getting into your other apps while you're not looking