If the batter rounded first and was on his way to second, award the batter second base. There will be less yelling if you leave the batter at first base. The batter hits a clean double. After rounding second base and starting to lay up the shortstop and runner collide. Yes, I would make certain he is not tagged out on the way back to the bag but the runner gets second base and not one foot more.
Every runner is taught to try and draw the obstruction call in a rundown.
When such a play happens between second and third base the runner changes direction and moving off the baseline is obstructed by the third baseman and then tagged with the ball. You probably noted that the umpire's judgment ways heavily on the decisions that will be made during and following an interference or obstruction call. This is part of what makes each call so open to scrutiny, questioning, and yes, controversy. If a subsequent play is made on the runner, you still let the play go - unless and until the runner is tagged out. You then kill the ball and enforce penalties as per rule.