Luckily, there is one herbicide that actually works well against violets and can even kill the flowers without harming your grass -- triclopyr. Triclopyr is a selective herbicide that effectively ...
They tolerate almost all hormone herbicides (MCPA, 2,4-D, clopyralid, dicamba, triclopyr, picloram), and speedwells are about the only weeds which survive a triclopyr/picloram mixture (Victory Gold).