You are using a Backup from the Primary PC restored to your Secondary PC?
You are not using the MC Media Server functionality?
This is not a good idea, and is fraught with difficulties. Both PCs would need to be set up identically to find all your media, with the same paths to media and so on.
Cover Art is not backed up with a MC backup. If it is stored next to the media, and all paths are the same, and you use a backup from the Primary, restored to the Secondary, then the Secondary should find the Cover Art.
However, if the Cover Art is stored in the directory defined in Options, which is separate to the media file locations, then the Secondary PC also needs access to that Cover Art location. If you are using the default location, that would be under the User directory structure on the Primary PC, and would not be available to the Secondary PC, due to Windows permissions.
So, if none of the above helps, describe exactly what you have set up, and how you are using MC on the two PCs. Include all your Cover Art settings in Options.