Weird base running play.

[Mark T. DeNucci, Sr.]

I think I blew this play and would welcome a ruling using NFHS Fastpitch Rules.

Girls' 14U, one umpire (and the temperature was close to 100F, meaning my brain was fried by the time the game was half way over), and this play took place in the fifth inning of a seven inning game.

Runner on first base attempts to steal second. The catcher makes the throw to second which was caught by the shortstop. I tried to get out into the diamond as quick as I could and from my position determined that the runner was safe and signaled very loudly that she was safe. The shortstop immediately throw the ball to the pitcher who was not in the pitching circle. At this point the runner must have thought that she was out and proceeds to walk back toward her team's dugout (on the first base side) at which point her first base coach tells her that she is safe. The runner thens starts to run toward first base while the pitcher who is still not in the pitching circle throws the ball to first base. The runner beats the throw to first base. I the runner stay at first base and told the pitcher to pitch to the batter.

What is the correct ruling?