Violets (Viola papilionacea) are great in shady areas where not much else will grow and where they can be controlled. But they can easily get into areas where we don't want them, and, once established, they are very difficult to get rid of. Here is the link to an Extension brief on getting rid of violets:
Controling Violets in the Lawn
Notice that the brief recommends triclopyr. Be sure to read the label carefully and make sure violets are listed as a target weed. Also, broadleaf herbicides such as triclopyr can drift onto nontarget plants and cause damage, so be sure you spray on a windless day.
Probably the reason you are not having luck with herbicides is that most herbicides work best in moderate temperatures, and most weeds (violets included) are more susceptible to herbicides in the early fall.