If Steffon Baratheon never died I think Tywin and the King's relationship would never have gotten so strained. Reading about them I sorta picture them like Ned/Bob/Jon Arryn in their rebellion days
At that point though, when Steffon died, the mad king was already starting to get jealous of Tywin and sent Steffon on that trip to find a bride for Rhaegar, which was one of the main points of contempt that strained the relationship.