Hopefully this picture will make things clearer:
https://i.imgur.com/338S7X6.jpg
So from a clean Retroarch install, what do I need to have checked prior to install?
I might have a solution to your multiple core issue. You said you would like certain games to load with certain cores, right?
1) Ok, drop Retroarch (RA) in Hakchi (HC) and add all the cores you want or need. If you already did that, then fine.
2) Make sure that you add --retroarch in the commandline of the game you want to load with RA, otherwise it will load with the SNESC's regular emulator. If you already did that, then fine.
3) Turn on the SNESC, load the game in question, press Select +Start to enter RA's menu. In the root of the menu, go to "Load Core" and select the core you want to use for this game. Then go back to the root of the menu, go to "Quick Menu" and press on the "Save Game Overrides". You won't get a confirmation or anything, but that should save all modified options for that game only.
Now, to test if it worked.
Press Down + Select to exit the game, then load the game again. Press Select + Start to enter RA's menu and check if the core you selected is still selected. If it is, great. Exit the game back to the SNESC's menu, and load a different game that is also supposed to load with RA and that you want to load with a
different core. Press Select + Start to enter RA's menu and check what core that game is using. If it's using a core you don't want, then change it to the one you want, then go back to Quick Menu and hit Save Game Override. Exit the game back to the SNESC menu.
Now, open the first game you modified and check what core it's using. If it's still using the same core you selected the first time, then great, the process worked. If it the core changed to the core of the second game you modified, then I guess you can't set cores to a per-game basis as you can with other options.