Have the USA not make drugs illegal in the first place. Mexico's current problems is due to the power and influence of drug cartels, who thrived by smuggling drugs into the USA. The USA should have learned its lesson after Prohibition in which the ban on alcohol led to the rise of organized crime there.
Why the USA still bans drugs is a head-scratcher. I believe in personal responsibility. If you are aware of the negative side-effects of certain drugs on yourself and you still want to use them, then it is your right and on one else's business. Making all kinds of drugs be legal after the age of 18 (with a notice sticker put on drug packages about the negative effects of drugs) would help Mexico and other drug countries like Columbia immensely by eliminating the drug cartels which then could be bring law and order back and stability.
While I fully agree that Mexico's current troubles stem largely from the ill-advised 'war on drugs' (and while I also agree that whatever drugs any adult person chooses to use is his own business and should be legal...), I also think that Mexico has socio-political issues that go back a long way. Removing the OTL US drug policy would certainly benefit Mexico, and all of Latin America, but it would not solve every problem. Mexico, from its very start as an independent nation, has suffered from political infighting (which often erupted into civil war) and had to deal with a series of successive coups. For Mexico to be truly 'saved' from its historical problems, that issue will need to be addressed.
In my opinion, a strong start is the best guarantee for success. Compare, for instance, the USA, France and Mexico. The USA really lucked out: when the original political framework didn't function adequately, they managed to peacefully alter it and introduced a consitution. The first president was an honest and capable man, who set a lot of inspiring precedents.
Then look at France. The French, following their revolution, tried out several mercurial political systems in rapid succession, ended up with a reign of terror, and then had a strongman assume control. Then the monarchy was restored, abolished again, another emperor got crowned, was deposed again, the country was occupied during WWII, and afterwards finally managed to become the stable republic it always wanted to be. But it took a while.
Mexico got it even worse than France, and due to a combination of factors, never managed to become truly stable and prosperous. Would it have had better chances without US drug policy messing things up? No doubt about it. But whould that have solved everything? Don't be so sure.
I firmly believe that if both France and Mexico had gotten off to a good (read: stable) start, like the US did, they would've had a much better chance. So to 'save' Mexico, my advice would be: start early. Give them a solid constitution from the get-go. Prevent Iturbide from crowning himself emperor. That, basically, solves the fundamental problems that Mexico has been struggling with ever since.