I've thought about this before, and I think the biggest result of Texan independence was that it demonstrated Mexican weakness to the US, making the US bolder. If Mexico defeats the rebellion, US leaders are going to go into the inevitable US/Mexico conflicts less convinced of their superiority. Result: two or three small US-Mexico wars. Texas is going to be US, Utah (whether Mormon or not) likewise. California (north and central anyway) is also likely. Mexico could possibly keep New Mexico, Arizona and southern California. This would probably change the whole dynamic of US-Mexico relations. Mexico would not be perceived as as weak (and with several small wars they would get the chance to improve their military performance

), although the US is still going to be stronger.