I don't have experience booking with consolidators, but I would be surprised if they didn't allow you to cross to both sides of the island. Perhaps you can try to contact the company handling it and confirm. Maybe they just have standard language saying no international driving, for example. You could easily go to the other side without noticing.
Thrifty and Hertz both suggest that it is no problem going to both sides. I would be very surprised if any company on the island forbids it, but perhaps your desired insurance is causing an issue.