I know that she was feuding with Alyssa Milano and Shannen (or it may have been Alyssa, I don't entirely remember) allegedly gave the producers the ultimatum "either she goes or I go". And considering that Shannen had already been fired from 90210 for allegedly being difficult to work with, it was quite easy to tell her the bounce. But confusingly, Shannen directed the final episode of Season 3. Plus, Shannen got along with Holly Marie Combs and Holly was apparently so upset by Shannen's departure, that she wanted to leave herself (but she couldn't get out of her contract).
That particular episode really sucked. Shannen Doherty is famous for being an absolute bitch when the cameras aren't rolling. It's one reason she's gotten so little work in the past 30 years. I think she directed her character's last episode because she wanted to do it right. It's a really shitty story about why Pru Halliwell died.
See, she and Piper fought a wind demon, but a mortal caught it on tape and sold it to the press, so then humans became aware that witches existed, since there was now proof. Basically, the Halliwell house got mobbed, with everyone wanting a piece of the magic, and demanding that the sisters solve all their problems: basically, their worst nightmares come true. One of the unwelcome visitors was a crazy woman who demanded the sisters solve some problem of hers, and when they told her to go away, she did...and came back later with a sniper rifle, and shot Piper in the stomach, killing her.
I think Phoebe either went to her boyfriend, Cole (who she didn't know was a demon at the time) to find a way to turn back time and fix this, or she had Leo, the girls' Whiteliner do it. Either way, a price had to be paid for that. So when time was rewound back to when Pru and Piper were fighting the wind demon, in the new timeline, it blasted the two sisters out the front door and got away. Piper was knocked out, but Pru had a serious head injury (there was blood coming out of her ear) and she died. So the secret of witches was preserved, but a sister was still lost in the end.
Shannon then felt her contractual agreements weren't being honored and her courtship between Spelling had waned. She felt the the three actresses should work towards a less "soapy" alternative. Earlier episodes show this transition into a crime/supernatural drama, into a camp soapfest. Shannon felt that her time on the series was at an end, and requested to be let go from her contract. She did feel the show wasn't as good as it could have been.
Alyssa and Holly were at odds over what they should do. Alyssa felt the show was fair at giving storylines and wanted to keep the trajectory of the viewership. Holly felt obligated and a sense of friendship with Shannon and wanted to ban together to work towards a mutual ground with production. Because of this tension, there were some hard feelings around, mostly between Holly and Alyssa.
Alyssa's contract of course had been renegotiated as well as Holly's and that is why the two stayed longer. Rose came in around this time, and the show survived the shake up with all cast feeling happy about that.
Shannon left with her rights intact to receive royalties and percentages from the show, and she didn't care if they let her go. She had money still coming in from the series run, and the DVD sales. So in all, she made a lot of money. Also, her reputation remained intact as well, she felt that her time on Charmed showed that she could be professional.
I think you may need to rewatch a bit. The crazy lady didn't have a problem, she wanted to be part of the Halliwell coven. When they sent her away she got a gun and shot Piper.
All the sisters knew Cole was a demon at this point. A scheme was hatched to ask the Source to have Tempus turn back time since Tempus was the only one who had the power to do it.
Cole took the proposal to the Source since all magic was under threat if mortals knew about it. The Source agreed, but after Cole left ordered Phoebe's death as soon as time turned back. (as I recall, nothing ever came of that order. )
Shannon is difficult but does NOT have the reputation for being a bitch when the cameras aren't rolling. Most actors praise her for being a professional even between takes. Her problem is that she does not get along with people higher up, in this case producer Brad Kern. They basically had creative differences and Alyssa used that to her advantage.
A Dancing Boy Blind: While I'm on the subject of the college, and not I guess a blind or anything, but who applied and was rejected back then? This one actress, known today probably more for her activism than her acting. She was the star - at least I'm sure as far as many of the men and boys in the audience were concerned - of this long running network sitcom back in the day. She is also known for her feuds, apparently driving this one actress to quit a certain later show, only to be replaced by another actress with whom she didn't get along. All that came up again late last year regarding a major celebrity scandal/divorce. You have to wonder just how bad her grades were. I mean, being who she was, you'd have to otherwise conclude that all she had to do was spell her name correctly on the application to get in. Actress: Alyssa Milano
Network sitcom: "Who’s the Boss"
Later show: "Charmed" (Shannen Doherty, then Rose McGowan)
Shannen ended up getting the last laugh as even though she was no longer on the show, she was still getting money from Alyssa and Holly's work in the seasons after she left.
I remember reading something from one of the staff that worked on set. He said that the writers hated Shannen because she was always butting her nose in and making them do re-writes, essentially guiding how the episodes should go. It wasn't until after she left that they realized she knew what she was talking about and that she was right.
You can sort of see this in the subsequent seasons which veered off into unrealistic (yes, I know, it was about witches with powers) fantasy. I felt the seasons after Shannen left were unwatchable.