I own the H4 and it couldn't be much simpler to use, the H2 is easier still since you don't have to decide whether to use it as a two or four track.
My biggest beef with either is the tiny display, but as you can essentially just push the record button ( somewhat large ) and go, that might not be an issue.
The H4 automatically makes a new file each time you press record, so you can record a performance press stop, press record ( new song ) hit stop, etc. When your finished each "song" is it's own little file in the order you recorded them.
They both have USB so getting them into the computer is relatevely painless.
I use mine as an interface to do multitrack demos for my band ( that's another affair altogether ) and I would recommend a more sophisticated device if that was to be its' main function.
For your ( wifes' ) purposes I think either would be fine.
Hope that helps
S.