I don't think she was right, but I don't think she was wrong, either.
She had just killed her boyfriend; Kendra, Slayer #2, who reminded her that she was NOT alone in the world, had just died; she was wanted for murder; her mother had just kicked her out of the house...I mean, can we really blame her for leaving? I don't think her actions here can be described as bitchy or whiny.
Also, I disagree about not giving Joyce enough time to come to terms with it. Maybe Buffy hadn't given her enough time...but she hadn't HAD any time. She was right smack in the middle of end-of-the-world stuff. What was she supposed to do? Have tea, sit down and talk about things, let Joyce sleep on it before saving the world? She HAD to leave right then, and Joyce had told her not to come back. When your mom says something like that, right in the middle of a crisis, and right before a greater crisis, it sticks with you. I think Buffy truly believed she couldn't return to that house...and once she was gone, it got harder and harder to return.
Of course, my opinion there isn't helped by the fact that I really hate Joyce. Her whole attitude in general just bothers me, especially during these episodes. Like when she told Giles that she blamed him for Buffy's leaving...riiiigghht, don't blame yourself for being a completely oblivious mother or kicking your daughter out, don't blame your daughter who actually did the running-away, blame the man who was just doing his job to defend the world from evil. :rolleyes0
I do think she should have contacted someone in Sunnydale and let them know she was okay. But I also understand that doing that would have been very difficult. She needed time, some serious alone time, in order to cope with all that had happened. Besides, it wasn't like it would have been the same situation if me or one of my friends had left town...she was the Slayer, they knew she could take care of herself. As Giles had said, Buffy was the most capable child he'd ever met.