They want Alice, Bella, and Edward. They think Renesmee will not be able to control her thurst and thus for expose the vampires. The Volturi is the most powerful group of Vampires because of the most members special talents because of Bella's power they are weak against the Olympic Coven. So destroying them would put them back on top and not have the fear of being over taken. The Volturi do not like how the Cullens don't abide by the laws and are trying to find ways around them. Such as, exposing vampires to Bella and then not changing her, having an alliance with werewolves, and having an immortal child.