The Volturi are forced to resort to Plan B after Caius kills Irina for falsely reporting Renesmee as an immortal child. While they may be power-hungry vampiric dictators, they like it when their subjects are unaware of (or at least unwilling to fight against) their manipulative games to secure power. When people feel oppressed, they are much more likely to band together to overthrow a tyrannical government. If the Volturi can say, “Well, they attacked first, after we did justice,” then they can portray themselves as heroes.
When that doesn’t work, they move on to Renesmee. The Cullens just proved that she is not an immortal child (a child who was turned into a vampire by a bite). But the Volturi are quick to point out that they know nothing of Renesmee’s species, which could pose a similar risk to the immortal children who once threatened to reveal the existence of vampires due to their impulse control. Given the vampire history involving these children, it wouldn’t be difficult for the Volturi to convince their subjects that they needed to kill Renesmee to be safe.
Then why do they so easily allow her to escape the scene with Jacob? Nobody tries to go after her, and Jane doesn’t try to torture Jacob so someone can catch Renesmee. If the Volturi want to gain the upper hand, all they have to do is make one proper move against Renesmee before the fight begins. She’s everyone’s blind spot, and going to extreme lengths to save her might be enough for more than a few Cullens to make a sloppy mistake that can’t be recreated in a vision.