The dead ball rule

[hawk0213]

As a young coach sometimes my stubborness gets the best of me, and I was thrown out of a game for arguing a dead ball call, I regret the result but I would like help confirming my purpose.

Before the game we go over groudrules and the opposing coach said anything that passes by the fense(extended) in foul territory was a dead ball.

Late in the game a ball was hit down the first base line it deflected off the first basemen's glove and went into the dead ball area in right field. Our right fielder put his hands up to signal it goin out of play, NO umpire called the ball dead, runners were continuing to run, and so our right fielder went and grabbed the ball and threw it in. He calmly walked in called time and asked the umpire why the ball wasnt dead. By then I was out there also and the umpire says its not dead because the right fielder played it. I was under the impression that a dead ball isnt optional and up to the fielder's discretion.

If I am at fault please let me know.