While Sam Houston originally wanted to join the United States of America, once he saw the atrocities and ineptitude of the US Armies during the Mexican-American war, he opted to remain independent.
Following the war, Texas engaged in wars against Mexico, eventually capturing all land North of the Rio Grande and on a straight line across from the Gulf of Mexico's northern coast to the Gulf of Calfornia's northernmost coast. Later wars acquired Sonora and Chihuahua for Texan control.
Later leadership decided to turn against the US, and in the Great War made minor territorial gains, but in the Texan-American war, lost entirely, and the United States has integrated all Texan Territory as states of the Union.