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.

If the ball was not *obviously* out of play, the umpires might not have been in position to make an immediate call due to bad angles, responsibilities at other bases, etc. In that case, he should have been moving to verify that the ball had, in fact, gone out of play. If your fielder plays it before he can make the call, too bad for you. Coaches should instruct the players to leave a dead ball lie. You're more likely to get the call if you can point to a ball on the ground and then argue that it is out of play.

You didn't include a key piece of the story. Did the umpire say that he saw the ball in dead ball territory or go past the dead ball line?

If he says that he saw it go into dead ball territory but wouldn't call time because you fielder, after seeing he wasn't getting the call, continued to play the ball, then the umpire misinterpreted the rule. If you protested the call based on his interpretation of the rules, you might have a case.

If he says he didn't see it go into dead ball territory, for whatever reason, you have to live with the call.

It should be a dead ball with time called immediately as soon as it goes past the line into dead ball territory.

Dead ball area must be clearly marked
 

Was there a chalk line there signifying where the fence line extended should be? If not, I'd be hesitant to call the play dead unless it obviously crossed the line (with no chalk line, how can I be sure). Are you saying the ball crossed the line by several feet (making it obvious), or not far enough that the umpire could clearly tell?

To protect yourself in the future, put a chalk line down. We have several high schools here that have tarps in live ball territory that they don't want players to step on if they should make a play near it (funding issues). Several instances happened this year during pregame, when the coach says "They can lean on it, but they can't step on it. If they do, it's dead." I'd have to say, "not unless you make that a dead ball area, we have to play it live." Just like a media area in the field of play - if media are present, they have to stay in that designated, pre-drawn circle.

Keep this in mind, no ground rule can supercede a book rule.