The Punic Wars were a response by the Romans to Carthaginian expansion in Sicily. According to wikipedia, if the operations that the Romans stopped had continued, Syracuse would be the only hurdle that would have to be crossed before complete control of Sicily (and we know from OTL that once the current king died his successor would ally with Carthage).
Based on OTL I can say there is probably a couple chances for the war to be prevented. The Senate deadlock could be moved in the direction of non-war, or the public forum could push to prevent the war. Perhaps the Cisalpine Gauls assault the Northern border, drawing resources. Perhaps Syracuse allies with Carthage earlier, and butterflies the conflicts that lead Rome to intervene.
Based on OTL I can say there is probably a couple chances for the war to be prevented. The Senate deadlock could be moved in the direction of non-war, or the public forum could push to prevent the war. Perhaps the Cisalpine Gauls assault the Northern border, drawing resources. Perhaps Syracuse allies with Carthage earlier, and butterflies the conflicts that lead Rome to intervene.