The Americans lose the War of 1812 badly. A more persuasive Hartford convention ensures an independent New England Confederacy.
Santa Ana is a better person and politician. He is elected to the office of the presidency and serves a stable term, paving the way for peaceful succession of several presidents.
In the early 1840s, Mexico goes to war with a severely weakened United States (Virginia, both Carolinas, Georgia, Alabama, Mississippi, Lousiana, Tennessee, and Arkansas). Mexico annexed Louisiana and Arkansas. Mississippi is formed into a protectorate by Mexico.
Mexico continues to industrialize while the United States become a backwater governed by a fragile system ruled by planter class strongmen. Veracruz becomes a symbol of hope for those looking for a better life.
By 1900, Mexico is the guardian of Central America and one of the top exporters in the world, stretching from Lousiana to Alto California to the Yucatan.
(Best way I thought to have the USA to be dominated by Mexico)