the Confederacy forced Mexico to send troops
But if the Confederacy is already in a life or death struggle with the US towards the end of the Second Great War, then how could the Confederacy possibly "FORCE" the Empire of Mexico to do anything? My recollection was that the Emperor of Mexico agreed to send troops northward because Mexico was a member of the Entente alliance (as was the CS, Great Britain, France, and Russia), the Empire of Mexico was ideologically in lock step with the CS regarding their pathological hatred of the US, and also because the CS has earlier provided the Mexican Empire with modern weaponry.
The US has at least a dozen states damaged in the SGW, Philadelphia was nuked, there's the massive economic costs in maintaining the occupation of three separate areas
From what I recall, Ohio and Eastern Pennsylvania were occupied by the CS, and that Pittsburgh was the sight of a major battle which destroyed much of its industrial infrastructure. However, the entire West Coast of the US is untouched by the war, including the industrial zones surrounding Los Angeles, San Francisco, and Seattle, and I don't recall reading anything about Detroit, Michigan being knocked out by Confederate forces? While I admit that the damage caused in Ohio (center of tire manufacturing in OTL) and Eastern Pennsylvania would have somewhat weakened the industrial capacity of the 191 United States, I don't that the temporary loss of manufacturing capacity from Ohio and Pennsylvania would have been the debilitating blow some would like to make it out as. In OTL both San Francisco and Los Angeles are a hubs of automotive manufacturing, ship building, and also airplane manufacturing as well as steel. There would also be lesser manufacturing centers sprinkled here and there about the country, for example, Studebaker once operated an auto assembly plant in New York City during the 1920s & 30s, so is there any reason to believe that a similar New York auto plant wouldn't also exist in the 191 universe?
However, the bomb detonated on the outskirts of the city, and no federal building were destroyed, and the city continued to function.
the massive economic costs in maintaining the occupation of three separate areas (Canada, Utah, and the ex-Confederacy),
In actuality, following the end of the Second Great War, the US military would be faced with the daunting task of maintaining occupation troops in the following areas: the defeated Confederacy, Canada, Texas, Sonora and Chihuahua, Cuba, Baja California, the Sandwich Islands, Bermuda and the Bahamas. However, I believe that manpower shortages would be the biggest concern, and not financial costs, as the government can simply print more money, or make the occupied territories bear some of the financial costs of occupation.
The political realities of the post-war settlement means that the US will have to bite the bullet and keep the Mexicans under their monarchy
I must respectfully disagree on this point. In the 191 universe there is a war within Mexico occurring during the 1920s known as the Mexican Civil War in which anti-Hapsburg rebels attempt to overthrow the Emperor, but there efforts are stymied by Confederate mercenaries sent to fight on the side of the Emperor. I think that this would indicate that a sizable percentage of the Mexican peasant class would be chomping at the bit for an opportunity to do away with the Emperor and his foreign backers once and for all. With France and Great Britain no longer able to support the Mexican Empire, I think that a feather could have knocked the Emperor off of his throne. Also the selling of Sonora and Chihuahua to the Confederate States to pay off a foreign debt was unpopular with the Mexican people (How Few Remain - Mexican officers crying as their flag is lowered for the last time) so I think that there is plenty of indication that the Empire of Mexico was a fragile regime which could not last long without support from outside. Again, given the fact that the US prefers to set up its puppets as republics (Quebec) what indication is there that the US would tolerate a previously hostile Empire along its southern border, when it has no obligation to do so. Simply find the right Mexican military officer, give him what he needs, and then he can overthrow the Emperor and declare the Republic of Mexico. As I said earlier, I think that the US can garner a lot of favor from the new Mexican regime be returning Sonora and Chihuahua, as these two regions are largely mountainous desserts with little potential.
I don't think Texas will return to the US
But why not? An independent Texas makes sense in the 1840s, but not really so much in the modern industrialized 1940s. In OTL, back in the 1800s the independent Republic of Texas was saddled with huge foreign debt, and its currency was basically worthless, and Texas could not afford to build a proper army. So, how would that situation be any different in the 1940s? I think that the situation would be even worse for an independent Texas in the 1940s due to the fact that they've lost the western third of their territory to the US state of Houston, Great Britain and France are no longer powerful nations and can no longer provide assistance, and it is unlikely any foreign power (except for maybe Japan) would grant them diplomatic recognition. In short, an independent Texas in the 1840s at least faced the prospect of acquiring new territories and expanding its borders, but by the 1940s pretty much all of North America is already settled, and not even weakened post war Mexico is going to give any of its territory without a vicious fight. - I think that if the people of Texas are given the opportunity to regain the territories they lost to the US state of Houston, they are given the option of holding a stable currency (the US Dollar), and realize that the CS will never rise again, then yes, I think that most Texans would vote to rejoin the US by 1949 or so. The key is to turn Texas Whigs into US Democrats, and to give a few of them seats on the DNC committee.
I'm not really trying challenge anyone's beliefs regarding what may or may not happen following In at the Death, because no one can say that they are right on this topic and the other person is wrong. I'm merely to describe what I believe may have occurred in such a universe, and as much as possible I try to provide underlying reasons to support my views. However, I readily admit that my opinions do not carry anymore weight than the next person's. This is just a thought exercise which can go in a million different directions.