Could I create a system image on this laptop and then use it to recover the one that is being stubborn?
Are they networked? Looking at that /source: parameter it implies that you just need to point it at something usable. So, if it was pointing at the other's WinSxS, and it was the same version that you were trying to get wouldn't that be "usable"?
<eg> Then in that case you probably could even use the /LimitAccess option and save yourself having to connect to WU. ; )
Ref:
http://technet.microsoft.com/en-us/library/hh825265.aspx
<quotes>
Use the /Source argument to specify the location of the files that are required to restore the feature. The source of the files can by the Windows folder in a mounted image, for example c:\test\mount\Windows. You can also use a Windows side-by-side
folder as the source of the files, for example z:\sources\SxS.
If you specify multiple /Source arguments, the files are gathered from the first location where they are found and the rest of the locations are ignored. If you do not specify a
/Source for a feature that has been removed, the default location in the registry is used or, for online images, Windows Update (WU) is used.
Use /Source with /RestoreHealth to specify the location of known good versions of files that can be used for the repair, such as a path to the Windows directory of a mounted image.
If you specify multiple /Source arguments, the files are gathered from the first location where they are found and the rest of the locations are ignored. If you do not specify a
/Source for a feature that has been removed, the default location in the registry is used or Windows Update (WU) is used for online images.
</quotes>
The first quote was about the /Enable-Feature command's use of that operand but I would suspect that rather than having significantly different functionality the documentation is different to avoid being redundant.
Good luck
Robert