The House of Barcelona *did* rule Sicily. I assume you mean Naples in addition to the Sicilian island.
As for how? A PoD in the War of the Sicilian Vespers might be needed. When Pope Nicholas III - who supported the Sicilian and Aragonese cause - died he was replaced by a staunch ally of the Angevins. Have someone less French-friendly be elected, or have Pope Nicholas III survive a bit longer, and you might end up with something closer to a complete victory for the House of Barcelona in the war.