I probably don't have to tell you this, but just in case: There is no Second Amendment in Mexico. There are hundreds of Americans sitting in jail in Mexico right now because they had unloaded,legal, registered (in the US) firearms, or even because the cops found a single bullet in their car.
They have a "zero tolerance" law for guns, bullets, etc. in Mexico. Clean your car carefully before you drive off....
I don't know much about driving and dogs, but it's probably easier to drive long distances with dogs than with cats. On the other hand, one of our cats loves to ride, one tolerates it and the others hate it.
We will have to transport 5 cats to Panama, each one in a cat carrier under the seat, as I would never allow them to be shipped as "luggage". It will take us 2 trips!
You should really visit this web site: http://www.takeyourpet.com/
it has a lot of info and links about traveling with pets, including links to international regulations and procedures.