i am sorry you are facing some probmes with cuety and your fixtures, i get a look into the fixtures files, here are the results.
For the Core 3x1 the mode you want to use is using subfixtures but cuety do not manage them, that's why the mode is not showing up! If you want to use your core3x1 with subfixtures the best is to use 9vh mode and then patch 3 times the rgb mode...
For the Qwash i checked the manual and the cuety fixture file and everything seems to fit exactly... so it should work!
COuld you please describe with details what is going wrong when you are using the Qwash to let me get an idea about where the proble can be?