If the same exact app is compatible with your iPad 2 ( not an newer, updated for iOS 11 and later version, but a version of this app that is STILL compatible all the way back to iOS 9 ), you can attempt to try my procedures below.
I make NO guarantees thst this will work
There is a way to do what you want to do and it involves using an older, but still compatible with new iOS versions, version of iTunes that is still capable of saving actual apps ipsw files, like in the old days.
You will need to find, install and use iTunes 12.6.5.3 to do this.
iTunes 12.6.5 found in this link here.
https://support.apple.com/en-gb/HT208079
iTunes 12.6.5 for the Mac requires OS X 10.11.4 or later. Not sure of Windows PC system requirement.
You will need to use this older iTunes version and once it is downloaded and installed on your computer, at launch, hold down the Opt/Alt key on your keyboard while launching this older iTunee version, so you can create a new Tunes library.
BEFORE DOING the IMMEDIATELY ABOVE, if you use iTunes on a computer and already have an iTunes Library, you will need to find the iTunes Library folder on your computer ( usually located in folder labelled Music ) and, temporarily, move/copy this folder to another location so you do not accidentally write over your existing current iTunes library.
You can save/backup your newer iPad to this version of iTunes. It will save all or your apps from that newer iPad.
Once the backup is done, check to see if it backed up all of your apps under the Apps category in iTunes, usually found in the upper left corner drop down button that says Music, if you click on that button, there will be other options, such as Apps.
Once you have located and found these app/s that you wish to copy to your olded iPad2, drag a copy of these apps outside of the iTunes 12.6.5 window onto the desktop of your computer.
Eject this newer iPad from iTunes 12.6.5 and unplug your newer iPad from the computer and now connected the iPad 2.
If you wish, backup everything on that iPad 2 to iTunes 12.6.5.
Once done, drag those app/s copies you made sitting on your computer's desktop back into iTunes or more specifically, drag those app/s onto where it says your iPad 2 name in iTunes.
Drag those app/s right onto the iPad 2 name in iTunes and those app/s should sync to both iTunes and your iPad 2, IF they are, in fact, still compatible.
Let your iPad 2 sync to iTunes, then eject it from iTunes, disconnect your iPad 2 from the computer, then check your iPad 2 to see if the app/s in question were transferred to your iPad 2, or not.
If the app is there on your iPad 2, before trying to launch and use it, do a simple hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.
If the app did not show up on that iPad 2, OR, it did, but the app does NOT work at all, after the hard reset, then the app does not work and you can simply delete it off of your iPad.
Best of Luck to You!