She feel out with Lady Gaga in a war of words through media. She wasn't working with her, it wasn't to her face either. If Dannii was sleeping with Simon, neither of them were married and they were both adults, they did nothing wrong. Dannii is younger, prettier and someone that Simon wanted in his bed, Sharon was jealous.. Dannii stayed in that job long after her relationship with Simon ended and remained professional and never, ever spoke about it.
It's got nothing to do with the rights or wrongs of Dannii sleeping with the boss, the story was that Sharon was pissed off because Dannii was lording it over everyone because she was sleeping with Cowell.
Sharon had every right to be angry, she had been an XF judge since the show began, then all of a sudden, Dannii comes along and is Simon's pet. Minogue wasn't as innocent as she made herself out to be.