The app needs to have internet access in order to verify the license with Google. It won’t need to do this every time but occasionally in order to verify the purchase. Likewise the Google account used to purchase the app must be active on that device.
I hope this helps and sorry for the inconvenience!
Are both devices active with the same gmail account? If not, they would need to be in order to verify the purchase with that gmail account. If it is the same, what do you mean when you say “kids restricted accounts”? Perhaps another app is preventing access to the internet or perhaps you need to give permission for Baker Business 2 to access the internet?