Softball/circle violation rule
I have a girl on third no outs and the batter is walked. the batter runs down to first and rounds first and continues to run to second while the ball is thrown back to the pitchers circle. the pitcher turns around to watch the batter run from the plate after 4 balls where pitched and does not stop at first just continues to second without stopping. is this a circle violation or no.
What you are talking about is the look back rule.
When the ball is in the circle, the runner is not prevented from continuing to second in your situation.
If the runner stops between first and second, they must immediately choose a base to go to. As long as the pitcher does not make a play or attempt to make a play they must continue on to the base they committed to after they stopped. If they stop or hesitate to choose a base after they stop, they are out. A fake throw from the pitcher would be considered an attempt to make a play.