Hmm, it sounds like your Uru client (UruExplorer.exe) was replaced with the older buggy version (the non-gog, which had the mouse issue).
Theoretically, none of what you installed should have caused it. I think the only thing that does replace UruExplorer.exe would be the "Official No-CD Patch" (when on GoG you should obviously not install this).
Or are you actually trying to play on the Deep Island shard
? Because this will replace the executable too. Deep Island wasn't updated yet, so it still has the mouse bug (this will probably be fixed at some point, along with widescreen issues - in the meantime there is a workaround
for the mouse bug).
However note that you should NOT install Ages or the Offline-KI using Drizzle on a Deep Island game - it already has all of those installed (in the case of Ages, they are installed during linking). The only reason to use Drizzle on a Deep Island install is to convert Myst V / MOUL Ages.
Also, I'd recommend making a full backup of the original Uru CC folder. This helps with issues like these, as you won't need to reinstall everything
You can even play the game from any folder, as long as you start it with UruSetup.exe - this is particularly useful if you intend to play the normal Uru, the offline modded one, or even Deep Island. (At least, this worked in the older version of Uru CC; I'm pretty sure it's still possible with the GoG version).