Wild throw question

[Jhmoron]

This question concerns Little League girls fastpitch softball, Majors (11-12yo) division. I hope I get the terminology correct. Here's the situation:

My team on offense. Runners at first and second. On a passed ball I send both runners. Catcher scrambles for the ball and makes a throw to third to try to get the lead runner on the steal. The throw is not in time, both runners safe, now at second and third. In anger the third baseman fires the ball back to the pitcher who misses the throw. The ball rolls into the dugout. Umpire calls DB and awards one base to each runner scoring R3 and moving R2 to third. I call time and remind the ump that each runner gets TWO bases on a thrown ball going into a dugout. I show it to her in the rule book. She decides to let her decision stand as she called it but said she would review it with the head (of the ballpark) umpire. Two days later I see the ump who tells me that, according to the head umpire, she made the right call.

The way I interpret the rule, each runner should have been awarded two bases. And since the wild throw was NOT the first play by an infielder (the catcher's throw to third was the first play) the two base award should have been from where the runners were at the time of the wild throw, second and third base.

Am I right or just showing the naivete of a first year coach?