Thrown Glove Situations

 
With no outs and runners on second base (R2) and first base (R1), the pitcher attempts to pick-off R2, but the throw is wild and goes into left-center field. The shortstop begins to chase the ball and he also throws his glove at the ball. The glove misses the ball, but the left fielder retrieves the ball and throws R2 out at home. R1 ended the play at second base. Any action required by the umpires on this play?
 
Bonus question: In the above play, what if the shortstop had thrown his glove at the ball and the glove hit the ball? After R2 had been retired at home, any other actions needed by either umpire?
 
Call
If the thrown equipment does not touch the pitched ball, thrown ball, or batted ball, then there is no penalty. However, there are base awards if the thrown equipment touches the ball. The awards vary depending on whether the ball was pitched, thrown, or batted.
 
So in the first situation below, there are no penalties or awards. R2 is out at home and R1 remains at 2nd base.
 
In the bonus question, the thrown glove struck the thrown ball. In this situation, the ball remains live until playing action ceases. At that point, if the runners have not advanced two bases from the time the glove struck the thrown ball, the runners are awarded two bases. The runners are not protected beyond those two bases. So for the bonus question, R2 is awarded home (run scores) and R1 is awarded 3rd base.