what is the vaccination mexicans get when they're young that leaves a crater in their right arm?

It was most likely Small Pox. But it has more to do with the type of injector use. The military still uses these Aeration "Guns" for some of its vaccines.

For the general public kids are not given vaccines with a needle in their butt cheek. Even most "Gun" vaccines/shots are given in the butt so that you dont' get scars that are visible.

I don't think they still give it but the vaccine you're describing is the Smallpox Vaccine.

It wasn't only given to mexicans though. My parents and even my husband have the crater from the vaccine as well.

That's small pox, those are no longer done since small pox is considered eradicated.

small pox vaccination

BCG?