A PoD even further back than Barbarossa might be needed for that. When he was Emperor, the Italians had already been very unruly for a long time. Best bet is probably an Investiture Controversy PoD, but I'm a bit hazy on that particular period to say for sure.
Barbarossa's problem was that as soon as he crossed the Alps into Italy to quiet down the Italians, his German opponents would start messing around in Germany and vice versa. Quite troublesome, those Alps.