We have two versions of Go Button in the App Store, one that unlocks with an in-app purchase and one that is prepaid (which some people prefer, but also is necessary for school or enterprise MDM installs that don't support in-app purchases). They have to be separate apps because of the way the App Store works, but everything else about them is the same besides the way you buy it.
If you already bought the paid-up-front app "Go Button Pro", then you can redownload it for free from your App Store "Purchases" or direct from the App Store page on any other device that is logged in to the same App Store account. Here is the direct link:
After you have "Go Button Pro" successfully installed, you can transfer any shows and audio files you might want from the regular "Go Button" app into "Go Button Pro", then delete "Go Button" from your second iPad.
Brent