With your 2010 iPad connected to the computer and that version of iTunes being able to save the actual app,
If you still have the original Living Earth .ipa app file, for that year and model iPad and iOS version, and still using iTunes 12.6.5.3, you should be able to drag that Living Earth.ipa file into iTunes and then drag that app over to where your 2010 iPad is listed in the sidebar of iTunes and it should load onto that iPad.
If that .ipa file is a newer file that is NOT compatible with that old iPad, then there is nothing more to be done.
All older third party apps for iOS 5, 6, 7, 8, 9 and 10 are all pretty much non-existent and gone,,today.
Both Apple and third party developers have removed all these older apps from Apple’s iOS App Store servers.
There is NO way, today, to get any older apps for these 7-11-year old devices, today.
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Sorry.