Although the install instructions for SS2 state, don't uninstall SS1 and then install SS2 in the same game, I did it with a game I wasn't really playing anyways. I'm the kind of guy who gets curious about what happens, so I try it. Things were okay for awhile, everything seemed to be working all right. But then things started to go wrong; plots didn't build correctly, quests wouldn't progress, crashes were coming more and more frequently. Lots of errors and bad behaviour I have not seen in the playthrough where I started a new game with SS2.
Now then, if you want to continue to play two games with the different versions, download the Vortex mod manager from Nexus Mods (if you haven't already). Vortex has a beautiful profile system. You create a profile for each separate character, which includes their own save folder. Then you figure out which saves in the main folder belong to which character and move them into that folder. After you enable the profile, you can enable or disable whichever mods you want that character to use. I have one character who uses the SS1 mods and my newest playthrough using the SS2 mods. When I switch profiles, Vortex automatically disables everything that character isn't using. Makes life so much easier!