Does the run count?

[baseballmom]

11u travel ball. Runners on 2nd and 3rd, 2 outs. Batter hits the ball to center field. The ball drops, runner on 3rd scores, center fielder throws to home but runner from second beats the throw. Batter runs to second but is out. Does the last run across the plate count if the batter is out at second? 

[Velho]

Yes. The batter was out after achieving first base so this is a Time Play.

Since the runs scored before the batter was tagged out, they both score.

[Coach Carl]

This is the text of the Major League Rule (OBR - Official Rules of Baseball):

5.08 How a Team Scores

(a)  One run shall be scored each time a runner legally advances to and touches first, second, third and home base before three men are put out to end the inning.

EXCEPTION: A run is not scored if the runner advances to home base during a play in which the third out is made (1) by the batter-runner before he touches first base; (2) by any runner being forced out; or (3) by a preceding runner who is declared out because he failed to touch one of the bases.

Unless one of the exceptions apply, as long as the run scores before the out is made (not when it is called, but when it is made), the run counts. This is called a "time play" as Mr. Velho says.

Your runner who was out at second does not fulfill any of the three exceptions.