Umpires Fail to Call Infield Fly

With the bases loaded and no outs, the batter hits an easy infield fly to the pitcher. The umpires fail to call the infield fly. The pitcher unintentionally drops the infield fly, but he recovers in time to throw home.  At home, the catcher tags home plate (while holding the ball) to force out the runner from third base.
 
The defensive coach would also like the batter declared out because everyone (including the umpires) agrees that this was an infield fly. Surprisingly, the offensive coach says that if his batter is out, then he wants the runner from third base to be called safe.
 
What do the umpires do now?
 
Call
Even if the umpires fail to properly call an infield fly, the rule is still in effect.
 
The situation determines the out, not the umpire's declaration. It is the player's responsibility to know the infield fly rule (NF Casebook 7.4.1G and 10.2.3G).
 
In the situation below, B1 is out on the infield fly. Because the batter-runner was called out, the force was removed from all the other runners. Others runners must be tagged and since R3 was not, his run scores.