Metadata editing DAM software

Lightroom can do this, but not by default. If you turn on the preference that enables automatic writing back of metadata, then it will do it. It's off by default because the constant checking can have an impact on performance. If it's off, you can still make it do it manually at any time (select files and command S).

Also, an issue some people have with LR is that Adobe does not like to write metadata back to proprietary/undocumented formats (like most raw files) because of the risk of corrupting those files. So when Lightroom writes out metadata for a non-documented raw file, it writes it out to an XMP sidecar file. That means if you want to recreate the catalog in the future from the files alone, the program you use must be XMP aware.

Since JPEG, TIFF, DNG, etc. files are documented, LR writes metadata directly into those.

Lightroom tries to do a lot of things, so if the UI is not focused enough specifically on DAM for her, you could cross it off the list.

Photoshop Elements, like iPhoto, is consumer-level and does not address serious DAM needs.