Best POD is actually that Uday dies early on, before he can fuck up so much. He single-handedly caused two rifts in the family with his bullshit. And recall, Bashar al-Assad also had an older brother who predeceased their father. Said brother (Bassel) was, like Uday, a it of a wild character. (Although, unlike Uday, not a sadistic psychopath -- at least not to my knowledge.) Bashar al-Assad was, like Qusay, the younger brother, less charismatic, and nor properly prepared to be heir at that time.
If Uday dies in a timely manner, the Saddam can start prepping Qusay as heir, much as Hafez started prepping Bashar as heir in Syria after Bassel died young. Without the family feuds caused by Uday's scheming and paranoia, the potential for a stable succession is there.
You'd have to butterfly it so that Gore wins in 2000, though. Assuming 9/11 still happens, you'll still see American intervention in Afghanistan, but without Bush and his Neocon inner circle, a new invasion of Iraq is far less likely. So then Qusay stands to inherit the country in due time.