I am not sure if the computers at your wife's work are on
a domain or in a workgroup. The first thing to check is to see if the (Reconnect at login) box is checked. You may need to delete the old mapping and create a new one to check this. If they are in a workgroup make sure the Workgroup names are the same on all the computers who will connect to the share. Just right click my computer, select Network Identification and then properties.
You will probably need to create the same user names and passwords that the users use to login to their personal computer to the computer with the shared folder as Holocron said above.
To do this go to Start, Run and type lusrmgr.msc