Well said Sandshaker, also SUV are high on list of stolen vehicles in all parts of Mexico, a rental would make a nice target...as said in an earlier posting to this topic, getting a rental into Mexico, will be a big problem.
I don't know all the details, but I saw this done on my road trip down: Belizians had been to the US, bought small cargo trucks, old u-hauls etc., filled them up, put a car on tow behind. The truck is sealed and bonded when you enter Mexico and given a limited time to cross thru to Belize. Something to think about, see if someone in Belize needs to buy a truck or van, you split the cost of driving it down and your dogs can ride in your towed car.
Have some of your friends in Belize check there for you.
Good Luck Rocio