I want to restore iPhone data that didn't get restored a few weeks ago, but don't want to lose data since then

The sad and short answer is No.

1. Restoring to an old backup will erase any data accumulated on the phone in the meantime. There is no way to merge backups or such.
2. App-specific restores are possible for apps which offer some sort of cloud support. So if she is syncing her contacts with iCloud or Google they should still be here after the restore.

However, the long answer is maybe.

First, make a list of the programs where you do want to attempt to merge or replace her data. You will need to rename the current device so the backup is saved, then restore the device to get at the old data. At that point you can extract the "old" data to a computer. Then you would restore the "new" backup and merge the data back for each case where you could get it onto a computer.

You can see how this is tedious, prone to error, and requires you to learn the specifics of each app where you want to get your data. All great things to know, but you have to balance it against the time it would take you to simple re-create the data in the first place.

This also serves as the perfect use case for iCloud backup. In this case, you would never have not restored the backup since the cloud is so much more accessible than a computer and a USB cable.

• Angry Birds used to store the game settings in a file that you can use a utility like PhoneView to read onto the computer.

I would say - once you have a list of the apps you want to "pick" - come back and ask that single question - how can I access the saved game levels for game X and people here will step up if it's an easy google search or they know how to get that one file off the device.