A-Rod was wrong here, and showing disrespect after the games doesn't help his cause.
What did Braden do?? He shouted to him..." Stay off the mound, stay off the MFing mound". HArdly over the top stuff. Throwing his glove in the dugout, not on the field, can be attributed to being angry in the heat of a ballgame.
ARod is a GR1 douche. Yelling at infielders trying to catch a pop-up, hacking at a pitchers glove while being tagged. This is bush league behavior, let alone coming from a HOF talent.
Players routinely return to first base after rounding second on a foul ball. How many have you seen run across the pitchers mound?? Not many, if any. Its something you just don't do.
Keep in mind, the A's had lost the previous 2 games. They didn't want to be swept at home, and played with a bit of an edge. Nothing wrong with showing a bit of emotion during a game, especially when you feel as though you are being dissed. Especially in your home park.
