A few car rental agencies in Cancun and environs allow their cars to be brought into Belize, but most don't. At one time, National did, but I don't think it does any more. I'm trying to think of the agency that does permit it -- I believe it's called International.
Just a suggestion... Rent the car in Mexico and do the area up there then return it. Take the bus to Belize and get a car as needed inside Belize. I found it difficult to find secure parking and the car became a headache especially in Belize City.
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