Second Incident: Base ump calls their runner out at first base. Our first baseman made a long stretch for the ball. I thought she kept contact with the bag when she caught the ball and then pulled off the bag. The other coach asked for a second opinion and the plate ump asked the plate ump. The plate ump ruled the first baseman came off the bag and the player was safe. The base ump was torched. He was later overheard screaming at the plate ump in the parking lot, “Don’t you ever overrule me!”
Now that is something I have never seen before.
First incident - while he was right (you never explain another umpires call to a third party in any sport in a game you are officiating) - his way of handling it was incorrect. The correct response to questions on your partners call is "It was his call so you would have to ask him what he called" or "I didn't really see it because I was concentrating on what I was doing"
Second incident - Guaranteed this guy is also a Baseball Umpire. Baseball umpires will 'check' with their counterpart to add more 'confirmation' to their close call- they want backup, not change of call. They rarely - if ever - change a call based on a discussion unless that discussion is about 'I couldn't make a call cause I didn't see it'. I know a bunch of umpires who do both baseball and softball and I've had this discussion with quite a few of them ("I'll change a call in softball, but never in baseball")
And again - his way of handling it is out of line and incorrect.
I would suspect these guys just don't like each other and this is an ongoing issue between the two of them.