As someone who works and travels in Mexico quite often, I can assure you that the Mexican Federal Government is trying hard to stop the flow of drugs out, and guns in. It's entire future depends upon it. There is what amounts to a war going on down there between the drug cartels and the government. Many of the local police departments are corrupt and controlled by the cartels, who methodically kill anyone who resists. That is why the federal government there has been occupying many border cities and taking over the police departments. This has created a huge demand for weapons by the cartels, who openly recruit ex-military and others to join in a war with the government and other cartels. It is understandable that the Mexican government would like to see more gun control or a total ban in the USA. Really, it is not any different than the police thinking in some large US cities.
It IS illegal to haul drugs out of Mexico, and every northbound car, truck, semi, and bus heading towards the US is stopped and searched 4-6 times at roadblocks within 300 or so miles of the border. In contrast, we do nothing on this side to limit traffic going south.