Yes, Kelly went too far in her Twitter messages. She posted Michelle's real phone number and accused her of elder abuse. This is both unlawful and a violation of Twitter's policies. Morally, I can completely understand Kelly's anger and emotional response, but we still have to live within the confines of the law. Posting someone's private information is harassment, and making unfounded claims about alleged abuse is defamation and slander.
Kelly Osbourne's tweets went too far. She is being sued by her father's mistress, Michelle Pugh, for her statements, including providing her private number and mentioning she would perform sexual acts for money. She also accused Pugh of elder abuse. Although his daughter is clearly hurt, publishing these statements was not the right thing to do.
Kelly Osbourne has been known for being a spoiled brat, I wouldn't be surprised if she is just doing this to get some attention from either daddy or the media. Whatever Ozzy and Michelle did is their business alone nobody else, except maybe Sharon; has any business in it whatsoever.
No, Kelly Osbourne did not go too far expressing her dislike and disdain for her father's mistress Michelle Pugh when posting on Twitter. Osbourne is protected by free speech and has the right to express her opinions, whether they are negative or positive, when discussing her family's situation on social media.