Runners Leaving Early on Tag Up & Appeal Rules

Question
My team was in a situation yesterday where there was one out and our opponent had runners on second base and third base.  There was a line drive to our right center fielder that he caught.  Both runners tagged up and from my view both runners left early.  There was only one umpire.  The one umpire was up the third base line and had a view of the catch and the runner at second base (and I can only assume third base, but unable to watch all three points at the same time).  I had my pitcher appeal the tag-up from second base and the runner was called out for leaving early.  My assessment of that situation is 3 outs and the runner from third does not score.  The umpire agreed that there were three outs, but the run scores because I appealed second base and not third base.

So there are different question scenarios here.  1) do you agree with my assessment?  2) Could I have had more than one appeal on the play (there where two, because there were two runners) where I appealed either bag and got the benefit of the call in either situation?  If I appealed the third base runner first (where the umpire admittedly was not looking) is there then no question here?

I'm interested to know your thoughts and official assessment of this situation.  An observing captain on a team not in the game agreed with my assessment.

Answer
Michael,

Good questions.

What you have here is a timing play.  Even though the runner at second was put out on appeal in the same manner as a force out, it is not a force out.  Unfortunately your assessment is not correct because the out on appeal happened after after the runner from third scored.

Yes you could have had more than one appeal.  You could have appealed the runner at third for leaving early after the third out, if the umpire had ruled in your favor this would have prevented the run from scoring.

If you had appealed 3rd base first, then yes you would have no run scoring.