Trying to update via the home menu just launches the eShop, which will then prompt you to update before continuing.
If you create the emuNand after the games are installed, then then emuNand's title.db and other internal files will contain information on them, so they'll show up. Anything installed after the creation of the emuNand will only show up on the nand that it was installed on, though I believe if you attempt to install it on the other nand, they'll both use the same data location, meaning you only have one copy of the files that both nands will use (rather than having it take up twice the space). But if she doesn't have a Gateway herself, or another method of launching the emuNand, it won't do much good. You could still extract personal CIAs for the updates from the emuNand, and then install them to sysNand. That's the only way I know of to get the games updated and have them useable without hacks and without updating the System Version. I haven't looked into spoofing the firmware, so if there's a way to boot sysNand with a version spoof, access the eShop, and grab the updates that way, that'd probably be a lot easier.
Nintendo also just released System Version 9.8 tonight, which only partially works on the Old 3DS on emuNand. (According to
https://gbatemp.net/threads/new-firmware-update-9-8-0-25.389986/ , the select button to choose a game doesn't work, as well as the region free hack, but you should still be able to access the eShop with it, as well as play installed CIAs that match your region. So it's still useable for a throwaway emuNand if all you're doing is getting the updates.) New 3DS won't support it, since it's still limited to 9.5 for the time being.