How is a country incorporated peacefully by another without governmental conflict? Maybe a vote to join can take place between the 2 countries. The only real problem would be drug warlords and I believe we are still at war on drugs. A border at the Panama Canal would be easier to maintain.
Not all Mexican officials are "dirty" as in corrupt. If you look closer into Mexican politics you will see that there are quite a few politicians who try to get their country back on track. However, they have to fight US sponsored crime syndicates. And yes, they are US founded, not directly, but indirectly by the war on drugs, which provides them a huge source of money.
The US taking over Mexico won't do anything. Not only has the US Mafia shown very impressively in the years of Prohibition that the US isn't any more capable of getting rid of organized crime than Mexico, it has shown that the more brutal you go against crime, the more brutal and strong it becomes.
The best way to help Mexico would be legalizing drugs and pulling the financial rug under the feet of the crime cartels that way. Then you could create a trade agreement between North and South America that includes high wages, high job security, very high environmental standards, a strong tax system that allows both states an effective infrastructure rebuild, and import taxes towards states outside the agreement so the overall wealth in both states can grow.