You could look into the possibility of doing a one-way sync of the library from the Synology NAS to your wife's laptop at windows startup.
Another alternative might be for your wife to use the calibre-spy plugin to access the library on the NAS directly, it is read only so there's no problems with concurrent updates. But I don't think it provides any direct Kindle connection features - maybe they could be added. See ==>>
Index of plugins
Added: Calibre Server on the NAS is of course the other way, your wife might have to use a browser on her kindle to get books from it - assuming that's possible.
PS: There are probably other ways.
BR