Clarification please

[PGCougar]

Here's the sitch - 16 YO travel ball with NFHS rules:

One out, runners on second and third. Batter hits fly ball to Right-Center, RF makes a great diving catch, runner at third tags, but runner at second runs to third assuming ball won't be caught. RF throws the ball all the way to third, third throws the ball back to second base where the runner was called out for the double play.

After a discussion between HP and field umpires, they ruled that the run scored. They stated it was a "troubled" play - saying the throw was made to third before it was relayed to second, therefore the run was allowed to score despite the force play at second for the third out of the inning.

Could someone please help clarify the call and point me in the right direction to appropriate references? I appreciate everyone's help. I hope I explained the sitch clearly, and apologize in advance since I'm a basketball person and only a spectator in baseball matters.