This is my take:
1. Warning for coaching
Every player knows a player is not supposed to get coaching while playing. That even applies in local club competition. It is cheating. It may be hard to catch or prove (eg see the controversy over Andy Murray’s loss to Verdasco), but the rule itself is unambiguous. The only exceptions are team events such as Davis Cup.
In any event, Serena only got a “code violation” warning, which normally means nothing.
2. Smashing racquet and 3. Abusing umpire
The next two events are remarkably similar to what McEnroe did in his infamous match against Pernfors back in about 1990 (which I saw live).
In short, McEnroe had already received a “code violation”. The match is tight, and he misses a point. He bounces his racquet hard on the ground. You can hear the crack. A point violation is given, straight away. McEnroe calls the referee, and tries to argue that the racquet is not broken, and he plans to continue playing with it. He loses the argument. As the referee walks off, McEnroe apparently yells an obcenity. (It is hard to pick up on the tv replay, but apparently he did.) The referee straight away u-turns. Third violation. Under the rules at that time, a third violation was a forfeit, not just a game penalty, and hence McEnroe was thrown out.
The reason I set all that out is to show that it is simply untrue that Serena was treated any worse than a male player would have been.