The entire United States besides what Texas has is, well, united, so you would need a reason for Texas to be withheld from the Union, as well as for Mexico and the US to go to war while keeping Texas independent.
My best guess is that the United States guaranteed Texan independence (but didn't admit to keep slave state/free state balance), and then Mexico decided to invade. Nationalists argued that the US needed to save Mexico, and in the process America took California, and Texas took New Mexico. An independent Rio Grande Republic lasted until the Civil War analogue took place, when Texas cut a deal with France (assuming same Mexican intervention) to annex the backwater republic that was proving to be a hideout for so many Mexican republicans.
Within the next 100 years, a majority of the inhabitants are going to speak English, although the case might be true that a majority of *Texans speak Spanish as well.
To possibly explain one further thing, the capital (which was pitched around five different locations during the Republic's existence OTL) was located in Galveston until the 1900 hurricane wipes the city out, killing 10,000 in the process. Due to some political finagling, key politicians outside of Texas proper lobby for Santa Fe to be made the new capital in exchange for low/high tariffs/taxes/support for a bill continuing slavery etc., since the US happens to build a transcontinental railway through the city.