Transferring Apps from One iPod to another I had to have my daughter's iPod motherboard replaced, and in doing so have had to re-download all the apps she had.  That wasn't an issue until she tried playing one of the games, and it was like she had never played it before...when we tried connecting through her game center (it still showed she was on the level she should have been), it wouldn't work because she had an older version, and the new version requires her to connect through Facebook to save her progress...I refused to sign her up to Facebook (she's 7), so wondered if I could copy the app from my son's iPod (the version she had before the repair) and put it on her iPod?  Would it copy the older version so she can continue to play (and still have access to her friends through game center)?
You can't really transfer apps between two IOS devices with different Apple IDs, unless you are up for jailbreaking, then I cant help you.

If you want to get the version your son uses on your daughter's device you will need to sign into the App Store with the AppleID on his device. But that will give you all of his settings as well. As you can see, problematic.

However you mention an older version and the App Store will always download the most recent version compatible with your system. So you may end up with the same version you don't want.

Perhaps there is someone else who knows a trick or two that I am not aware of, but if not you may be out of luck.