Ok, I'm kind of trying to dredge up a memory here that wasn't very precise (by me) in the first place... So, please don't 'bite my head off' if I'm wrong;
But it seems to me that I remember from my pre-revisionist history that the Mexican-American War was fought primarily over Texas and California... But not because "american illegals" invaded them; The LEGAL settlers (by the then Government of Mexico's own definition) in both Texas and California (Hispanic and Non hispanic alike, in a general majority) voted to secede from Mexico's rule; either to become independent states or to become part of the USA.
Most of the Alcaldes, the Dons etc, the local mexican/hispanic elite, as well as the majority of the every day 'gringos' of both areas understood that their best financial futures were with the US, rather than Mexico which was sucking them dry through taxes, etc.
So, Remember the Alamo and all that. (There were a good many 'hispanics' fighting INSIDE the Alamo, and running around WITH Sam Houston, by the way).
When Mexico sent troops north to make sure that California and Texas STAYED under their rule, that coincided with the "Manifest Destiny" policy of the US government and people; So, with the excuse of supporting the freedom of the Californios and Texicans to secede from Mexico; President Polk eventually sent American Troops to aid the 'militias' of California and Texas (and the rest of the Southwest in general).
Sure, greed and the desire of America to expand are part of it, but you have to remember that none of the Southwest was particularly valuable in those days. There were a few places that produced a little wealth here and there but nothing really worth fighting for on strictly economic terms.... (Had they found gold at Sutter's Mill a few years earlier, that might have started the Mexican-American War all by itself, and made Mexico fight more seriously... But it didn't.... And so it was a short war that just wasn't important enough for Mexico to put up more than a token fight....
In 1845 Mexico probably COULD have won if they really, really wanted to expend the necessary resources. Their military was better trained and better equipped than ours, with fewer logistics problems, IMHO.
Anyway, that's the way I remember it; I'll admit I could be wrong about significant parts.
I think your account is the same as mine, considering! What some, not all Latinos in the USofA today claim is that the will "TAKE BACK" the southwest. If they want to "TAKE BACK" then they feel that someone or something "TOOK AWAY"! For decades the American LEFT has yapped that the "evil" whiteman took away land from rightful owners in North America. My answer has been "what ever is the greatest good for the greatest number" should pervail.