The dad is definitely a nuisance. That's why as a coach, you have to enter a psychological contract with the parents from the very beginning and let them know that when the kid gets on your court, the parents must SHUT IT. That's how I handle my students & their parents, and it's been smooth sailing so far.
As for the comments screaming "abuse", the kid is a trooper, she can probably handle it. How her dad treats her may not work on other kids who have a softer personality, but as long as she's tough enough to handle it, I wouldn't worry too much. In fact, a kid who talks back like that might even need a parent who is tough to keep her grounded as opposed to letting her go wild.
On the other hand -- as a parent, if you find yourself having to scream at your kid to do something right... it is 100% your fault, not the kid's. You either 1) don't have the coaching ability to fix the kid's problems or 2) never raised the kid right to be easily coached / motivated. There's not a single kid who was born hating tennis. Kids respond to their environment - and parents play a critical role in giving the kid either a reason to love or to hate the sport.
2 x Tecnifibre 325 VO2 Max
WeissCannon Silverstring @ 43lbs