Transferring Apps from One iPod to another
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.