I understand your frustration,  I, too, am fighting violets.  Unfortunately you will have to dig them in your garden.  And do so repeatedly as they spread through their root system and through seeds.  A weed killer would also affect your garden plants.  You can try weed killer products in your lawn.  Read the label to see if it is labeled for wild violets.  There is no magic bullet.  Only repeated digging and pesticides, where appropriate.  https://extension.umn.edu/weeds/wild-violet