No... only Mexico can prosecute a charge out of Mexico. Only a state can prosecute a charge committed in their state.  Neither has the right to overlap into the other's jurisdiction.However, most jurisdictions will enhance or bump up the punishments for repeat offenders.  This means that if you have already had a conviction for a DUI in Mexico, and then you pick up a new DUI charge in the states, they can increase the amount of punishment you would receive because of the prior conviction--- assuming they can prove the prior conviction.  The enhancements vary by state, but usually the first couple of DUI offenses are misdemeanors, and then convert to felonies after the commission of 2-4 offenses... depending on the state law where the last DUI occurs.