My take on things - coaching happens all the time. Umpires are well aware of where the player boxes are and you'll notice them looking between points and on changeovers, especially when the player is on the side near their coach. Unless there is something blatant, like a coach standing up and yelling "serve to her forehand" or something like that, the umpire will usually warn the player on a changeover and say that they're seeing or hearing things that may be interpreted as coaching and that it needs to stop. As a line umpire, on more than one occasion I've had a chair call me over and ask me if I could hear what was being said more clearly than they could. For a code violation to be given for coaching, in my experience, there must be ongoing signalling despite a warning or something blatant. I'm not sure if there were any conversations between Carlos and Serena earlier in the match.
But let's assume that the code for coaching was hasty and erroneous. Let's assume that she legitimately had no idea what her coach was doing or that all he did was give her a thumbs up. It's a warning. It means nothing. They had a nice conversation about it afterwards in which she explained her position and Carlos seemed to understand and sympathize and smile and nod. But he still gave the warning. You can't take it back. She's been playing long enough to know that. The warning was there. At that point, it was all out of Carlos' hands. The racket abuse was clear. There's no judgement on that. After the racket abuse, she let him have it. Twice. Once at the point penalty and again on the changeover. He took it, as he should have. And he took a lot. Then she crossed the line. Calling an umpire a thief is accusing them of being partial and attacking their integrity. That's a very clear line that you do not cross. I've taken a lot of crap from players of the years because I know that emotions are high and I know that they're the ones out there competing. What I have never taken and will never take is being accused of cheating, partiality or having my integrity questioned.
While the code violation for coaching might not have been the correct call, it was a warning, no different than a time violation warning. Serena should have put it aside and just played tennis. Her actions and her actions alone resulted in the rest of the fireworks that we saw today.