Dead ball - placement of runners

Question
Situation: (ASA 14U) R1 on 3B, R2 on 2B, R1 on 1B 1 out.  Batter hits a single to F9. R1 scores and R2 attempts to score.  After scoring, R1 immediately attempts to leave the field and opens the gate to the dugout. F9 is attempting to throw out R2 at home.  The throw skips past the catcher and enters the dugout through the gate that R1 was entering. Off. couch wants B1 on third and all runners score due to ball entering dead ball territory.  Def. couch wants R1 at 2B and B1 at 1B due to offensive interference (ball would not have entered dugout if R1 did not open gate, which by rule was necessary as all scoring runners are required to leave the field immediately). What is correct ruling? Where should runners be placed?

Answer
I need to make some assumptions to answer this.  I am sure you mean tha that R3 is on 1st.  R1 can't be on 1st and 3rd!

R1 is leaving the field. R2 is between third and home.  R3 is between 2nd and 3rd when the ball leaves the field.

There is no way that opening the gate is interference unless the ball is hit by the gate as the player opens it or the act of opening it physically interfered with a defensive player.  Just opening the gate to leave the field can't be interference if the ball rolls through the open gate.

The defensive coach is dreaming.  

The award for the dead ball out of play is two bases from the position of the runners from the time of the throw by F9.  Most likely placement is  R2 scores, R3 on third unless R3 had rounded 2nd by the time of the throw.