No problem with the dogs. However, the 'exotic bird' may be a problem. Actually, you might be able to get it into Mexico, but not be able to return it to the USA. I suggest that you contact customs in both countries for exact details. I sure can't help on this one but you might find your answers here:
Questions about taking pet birds across US/Canadian Border - BirdBoard.Com - Parrot Message Board & Pet Bird Owner Forums
Questions about taking pet birds across US/Canadian Border - BirdBoard.Com - Parrot Message Board & Pet Bird Owner Forums