I look up how to set ignore ownership.
"Ignore ownership" can only be set for a hard drive or a disk image, not for a folder, for example - the "Get Info" for my media drive looks like this:
This cannot be done in the Shared folder. The article I pointed to, explains how you can put a writable disk image into the "Shared" folder and set the ownership flag for this disk image. Then both can red and write the library.
When I originally installed Aperture I allow the install program to set the Aperture references, what should I have it set too?
I was referring to the settings in the import panel, when you import images into Aperture: in the "Aperture" brick of the import panel is the "Store Files" option; if this is set to "In the Aperture Library" you should be o.k. - all original images safely contained inside Aperture and managed by Aperture. I asked about "referenced" or "managed", because it can happen, that images get accidentally deleted, if they are stored outside the library.
Under "Get Info" I have set the permissions as read /write for my wife - to be honest she rarely opens iPhoto, so maybe best to set the permission to read only.
That is a good plan. Then you will not need the additional complication with ignore ownership, if she does not read and write to the library.
Try first the three "First Aid Tools" to repair any damage that may have been done to the library, select the library and hold down the ⌥⌘- keys while double-clicking the library.
Repairing and Rebuilding Your Aperture Library: Aperture 3 User Manual