The place where the crime happened is the place of jurisdiction. If the defendant on the criminal suit is in the US, then extradition isn't necessary. If he's Mexican and living in Mexico, that's another story. If there were different crimes committed in Mexico, then yes, it's possible that the defendant can be prosecuted there as well. Keep in mind, however, that jurisdiction over the defendant could be problematic for one country or the other.
The purpose of civil court
is to obtain monetary damages. The purpose of the criminal justice
system is to punish wrongdoers. If it's money that you want, while you can get resititution as part of a criminal disposition, it will be less money than a civil award because in criminal court you can't get damages. Also, if the defendant ends up in jail, you will wait for years and years for your restitution.
So there are practical as well as tactical decisions to be made.
As I have said, the DA will be handling any criminal case on your behalf, so you won't need a lawyer for your criminal matter. Given that, there is nothing stopping you from filling out a police report
-- you should do that any way -- and discussing the pressing of charges. Your lawyer has advised against it at this point, so if you value him, I'd ask how he feels it could hurt you/hurt your civil case. He should be able to tell you because he has all of the facts he needs.