Why won’t Sonic & Knuckles collection work on the windows 10 computer

It's actually quite likely that these games are relying on old 16-bit DLLs. A lot of early 32-bit software relied on old 16-bit DLLs for some functions, as they did the job, they weren't used in a performance critical part of the software and there was no need to look for 32-bit versions. (for example until fairly recently the install software was often 16-bit, so much so that Win7 actually detects that and silently replaces with it's own 64-bit version of the old DLL).

Have you looked at Windows 7's XP Mode? This runs an entire copy of 32-bit Windows XP within your Windows 7, letting old programs run within XP without the program knowing it's on a 64-bit Win7 machine at all, and as it's all integrated you will hardly notice that it's running in XP.

Windows 7's XP Mode: what it is, how it works, who it's for

I'm the author of SkipWE. I created a ZIP file which should allow you to run SkipWE without internet access. Simply download the file from the link below, extract it to your desktop (or elsewhere), then double-click the "SkipWE.exe" file. Hopefully that will work at your mother's holiday home :)

FILE: http://www.megaupload.com/?d=78RHS2UQ

Enjoy!

-PF