I had an umpire that emphaticlly told me my player missed the tag. When I told him my catcher had the ball and was blocking the plate and therefore the runner had to slide I was told to take myself back into the dugout or he'd throw me. I asked him to please ask the other umpire. I got thrown Second game in my life. All asked very politely (even the other coach went 'but why she didn't do anything wrong' and got threatened with being thrown herself!) At one point he tried to make me leave the complex but thankfully cooler heads prevailed and I was allowed to sit on 'this side' of the complex (ended up leaving anyways as I needed a nice long walk or harsh words were going to be said afterwards) To top it off? After the game the other umpire admitted to me that he would have told the plate he was wrong. The runner moved from the tag, which he saw at first base. After being told that I (lost my head) and offered the plate umpire my glasses as clearly he was blind. I hope he never umpires a game of mine (different association) as I will not get one strike called on me (and after doing that, probably deservedly so)
Most umpires are unreasonable when it comes to questioning their calls. There is nothing wrong with asking an umpire to go ask for a second opinion. ESPECIALLY when you have the coach giving you the reason why.
Please don't tell us that your first argument about this play was that the runner HAD to slide. That, of course, is an absolute falsehood. Runners are NEVER required to slide at any base, for any play, under any circumstances.
To the umpire that offered up his opinion of the play after the game, thus escalating an already tense situation...way to throw your partner under the bus. From 70+ feet away he was sure he had a tag because he "saw the runner move"? That's pretty weak evidence. Why use it to get an already fired-up coach even more fired-up? His long distance view was no more valid that the view of the umpire standing right next to the play (and probably quite a bit less so).
I would really have to question the professionalism and motive of an umpire that would basically tell an already upset coach, "My partner doesn't know what he's doing, but I do". Way to throw fuel on the fire...
In your defense, it does sound like maybe the ejection came too quickly and was unwarranted. And I certainly hope that no umpire would intentionally make bad calls against a team in future games, just because of their coach's actions in a past game.