"Monday, Monday ..."
(an old Mamas & Papas song....)
Is your mom's computer in the "Insider" program? You mention putting her on the fast ring (which is doing Redstone builds at the moment ... not particularly mature just yet, but that's what beta-testing is for). I can imagine that a permissions issue could be the cause, as we've surmised at a few twists & turns already. If the file can't be accessed, I can see that it might lead to an unhelpful (misleading) "not a valid Win32 application" error.
If your mom isn't in the Insider program, using the Win10 on your spare drive as a source for the DISM process might work, if the version difference doesn't interfere. We found out in our research earlier that DISM "cannot be used with Windows images that are more recent than the installed version of the Windows Assessment and Deployment Kit" -- that quote assumes that the DISM is being used for roll-out deployment - rather than repair -- but I'd guess that it might matter for the DISM.exe executable to be a version-match to the Windows image being repaired (the DISM.exe version used would be either the same, or newer, than the Windows image being repaired).
I looked a bit (again) at the file you mentioned earlier (psapi.dll), and since it looks to be a fairly simple library for device & driver information ... I'm thinking it's an innocent bystander, that happens to be accessed just before the problematic, inaccessible files that throw up the 193 error. The psapi.dll ("Process Status API") has a whole section of information for developers over on the Windows Development Center - if you want to have a look at that --
https://msdn.microsoft.com/en-us/library/windows/desktop/ms684884(v=vs.85).aspx
Trying the DISM from the spare drive might not work, but it shouldn't hurt, either.
Should that not work, it might be faster to go with a clean install for your mom's laptop. Unless she's interested in the adventures and misadventures of beta-testing, I'd guess she'd rather not be in the "Insider" program . . .
I'll stay tuned ....