Was this too much?

[canadaump6]

I'm bringing this situation up to inquire about what should happen with an ejected player after a game.

Adult league game, my team is on the field. R1. Ground ball to second baseman who overthrows first base and throws it out of play. Plate umpire sends R1 to 3rd and BR to 2nd. Immediately upon hearing the call, young first base coach starts yelling very disrespectfully at 65+ year old umpire, including the phrase "I am a former umpire!".

By now you can tell by the umpire's voice that he is provoked, p1ssed off and even a bit nervous. After a bit more yelling from the player, he tosses him. Immediately upon ejecting, the player gets in his face and yells "you're brutal" among other things. He actually points his finger at the umpire, and the ump takes a grab at his finger. Fortunately the player moves it away, but starts yelling "don't touch me! Don't touch me!". Nobody intervenes, but finally the player goes to the bench where he is greeted with high fives by over half his team mates.

The plate umpire, from on the field, tells him "you have one minute to leave the ballpark or this game is forfeited", and then looking at his watch "10 seconds are up already". Now another player starts yelling "he's got to get his stuff!" and "it's a public park you can't kick him out of here!". I believe that the ejected player did eventually leave.

My question is should an umpire be putting a time limit (ie 1 minute) on how long a player has to leave the park? Also, where do you guys normally require a player to go after he is ejected?