It’s not a gender issue. The coach let her down, and later admitted he was coaching, so the warning was appropriate. She argued over it but got no further penalty until she smashed her racket, which is an automatic point deduction.
She then somewhat unreasonably ranted at the umpire and called him a ‘thief’ for applying an automatic point deduction. He was perfectly entitled under the rules to deduct a game at that point for that outburst, and she gave him the opportunity to do it.
Basically, she was getting hammered anyway, and either lost the plot or decided to use the partisan NY crowd to try to intimidate the umpire.