Appealing a Tag Up

 
With bases loaded and 1 out, the batter flies out to left field for the second out of the inning. The runner at third base (R3) properly tags-up and scores. However, the runner at second base (R2), did not properly tag-up and advances safely to third base. The defense calls "time" and properly appeals that R2 did not properly tag up. The umpire agrees and calls R2 out for the third out of the inning.
 
The defensive coach reminds the umpires that R2 was forced to return to 2nd base to properly tag-up. He continues to help the umpires by reminding them that R3's run should not count since the last out of an inning was a force out (NF 9-1-1b: "A run is not scored if the runner advances to home plate during action in which the third out is made by another runner being forced out"). What do the umpires do?
 
Call
When the batter-runner is out before reaching first base (as in a fly-out), the force is removed from other runners already on base. In the situation below, the force is removed when B1 flies out. Further, R2 is not "forced" to return to second base in order to properly tag up. R2 is "required" to return to second base in order to properly tag up or else R2 is at risk to be called out upon proper appeal by the defense. Since R2's out is a timing play, R3's run counts.