You can't change their government from here, because they will not allow it anymore than we will alow them to change our government from there.
Sure we can. Put some control over immigration and things will change quite quickly. They would have to. Can you imagine how much more quickly changes would take place if even just a few million of the illegals who have been exposed to the American way of things were to be returned home? They're going to want cars, tractors, telephones, indoor plumbing --- all the things they never saw before coming here. They would be a big stimulus on getting changes going.
The Mexican government knows it --- and that's why it's so insistent on no controls ever being put into place.