I'd say the weapon itself could destroy Coruscant, if it got in range and was able to fire. Even if Coruscant had some sort of shield or were somehow more resiliant, I doubt the amount of resiliance would matter much, since being able to turn Alderaan into an asteroid field in one shot, implies it could do at least life-extinguishing damage to a much much more resistant target. So it's definitely a possible danger, and one that therefore would have been considered and made unlikely in many ways.
For example, they wouldn't have put Tarkin in charge if they had any notion that Tarkin would ever do that. Even if he did, I think it's most likely he'd be overthown first by some level of command and/or mutiny, even if he had a cadre of like-minded supporters. Assuming a certain level of intelligence, the Death Star garrison itself may have been given a split command structure with highly trusted leaders, so even if there were some mutineers, they would be outnumbered by loyalists. Order 66 shows precedent for this sort of contingency planning. Surely there would be an Order 1099 or something, or a standing order to take out anyone ordering the Death Star to go to Coruscant, or anywhere else fishy and not Emperor-approved. In Episode IV too, we see a meeting of a council of Imperial leaders on the Death Star. Vader chokes one of them, but if it were just Tarkin and he were ordering moves towards Coruscant, I'd expect the others to move to take Tarkin out.
Even if the Death Star command structure was all for going to Coruscant, getting close enough soon enough may have been an issue, as I'd assume the Emperor and the Imperial fleet would have considered the possibility and planned against it. It probably was prohibited from navigating near Coruscant, both by regulation and possibly by its own computers. The computers could have failsafes where trying to hack them or order prohibited moves would disable to navigation and turbolaser and send a warning to the fleet. Since Obi Wan, who had never heard of the Death Star before, was able to deactivate the Death Star's tractor beams, presumably there were ways that either computer failsafes or loyal crew could intervene to prevent the ship from destroying Coruscant. The fleet may also have been able to detect and counter its moves. A large Imperial fleet attack may have been able to focus fire on the turbolaser and take it out of action.
As for Vader, I wouldn't discount his ability to stop a renegade Tarkin. His novice son managed to take out the Death Star. He might have been able to take out the Death Star by similar or other action, but it wouldn't be certain... On the other hand, I don't know what it takes to target a "Force Choke", but given he could kill Admiral Ozzel by choking him from a distance, he may have been able to do the same to Tarkin just by getting nearby. The answers to this question suggest that he may not have needed to get close at all to choke Tarkin.
The Emperor too would have had some abilities to counter Tarkin, by forseeing his betrayal, and no doubt by other means. Certainly he would have thought of the possibility, and arranged for some countermeasures, at least as described above, if not moreso.