To take pet across the border into Mexico you need a valid health certificate - any vet should be able to give you one. Rarely are you asked for this but you could be.
When you cross back across into the USA, you also need a valid health certificate again.
You could, in theory, use the same health certificate for both crossings depending on how long you are staying in Mexico. The health certificate must be issued within 10 days of border crossing.
Again - any vet in Mexico should be able to give you a valid certificate. I've never had a problem - either way - with the vet knowing what to do. The question they always ask is "when are you crossing the border" because if you get the health certificate too far in advance, it will expire.
Charlene