Put mayonnaise and mustard in a bowl large enough to hold complete mixture, but shaped so that the mixture can be beaten with a fork. Beat mayonnaise and mustard until combined. Add olive oil slowly, beating all the time. Beat until mixture has returned to the thickness of original mayonnaise. Add Louisiana hot sauce, continuing to beat.
Add ketchup and keep beating. Add salt and garlic salt, beating all the time. Add wine vinegar (this will thin the sauce down). Beat this thoroughly, adding the lemon juice as you do so. Taste for salt and pepper. Place shredded cabbage, peppers, and onions in a large salad bowl.
Pour sauce over and toss well. This should be done about an hour before serving. Tastes even better the next day.