Iturbide doesn't declare monarchy and establish congress asap. Stays president so he can fix up mining to it's glory. Technically that is one of the hindrance on his effectiveness. Establishes centralism. After that things are good and running relinquishes dictatorial powers and establishes a congress then constitutional republic no military bravado can like handle office as long as they're in miltiary. Economy again pre revolution or suprasses pre revolution levels. Peace and order restored. Generals with less powers.
Also no Iturbide appointees of his frens and fam on military position. Unless they have skills. That alienated him with the military. With everything come in mind just have it good and have congress or the country fund his lavish lifestyle meanwhile competent or even semi competent handling of country will put the country in autopilot to prosperity.
Iturbide also bans immigration to Nueva Filipinas (Tejas), Nuevo Mexico and California both Alta and Baja. Gives feifs and huge tracts of land to his buddies and frens instead.
Then with Iturbide steps down or has his term ends, Santa Anna becomes President.
Santa Anna successfully compromised between the Liberals and conservatives, successfully putting g out the radicals and reactionary elements of Mexico. Meanwhile cultivating good relations with France and Britain, giving mexico access to more loans trade investment and cash further eco growth and dev.
Meanwhile with the cash they have developed quickly and has huge economic growth. Aside from that cash to the military to modernize train and arm it good it aside from that keep quality of soldiers good. Put competent peeps. That is not politicking.
Cali gold found earlier, uses indentured labor to extract it. Meanwhile Mexico taxes it.
With a powerful neighbor east and or south, also the north, I doubt the usa would even like declare war.