Manual extraction is the most natural and non chemical. After a rain use a weeding fork. Very therapeutic. My mother found it to be an excellent disciplinary tool. Funny what once was the dreaded punishment is now a stress release :)
my wife brought these weeds home from a trail ride on her horse about five years ago. put a small bunch in a planter on our porch. Looked fine. Next year noticed them in lawn. Next year worse. Last year so bad we ended up using my natural method weed killer. Tried to pull them out, first few years, but if you leave just one they come back even worse. I would save the energy weeding and just use a product that will remove them once and for all. Many of the new weed killing chemicals are not like the ones used years ago that lasted for years in the soil. Most break down quite quickly so no long term lasting chemical effects in the soil.
Pulling is definitely the best strategy. Wild violets have a waxy coating on their leaves that makes them largely invulnerable to herbicides.
oh my, if these are the wild violets that grew in my home town in N.C., I have to say, I love them....they put off the prettiest little flower, they take care of themselves, and they are ever so soft when you walk on them barefooted....my husband hates them, but I was so grateful that I could get them to grow here in Florida.....they remind me of my childhood days when my brothers and I would go out and pick these, daffodills, lillies and wild strawberries from the woodland areas....I will never get rid of mine.... :)