Not using nautical miles places it at about 1,600 but that's besides the point. If for comparison, however, Washington D.C. to Nuevo Laredo is 1,730 miles.
Puerto Rico is directly tied into the political structure of the US in a way Mexico never has been, but Puerto Rico still has a distinct linguistic and cultural identity. In OTL, people from foreign countries and free states immigrated to the former Mexican territories in far larger numbers than people from the slaveholding states. Until there is a direct rail connection to Mexico, sea travel will be the primary connection to the core Mexican territories. There would be some immigration to the core Mexican territories, but the majority of white immigrants will not want to be the minority in a largely Hispanic population, the majority of Protestant immigrants will not want to be the minority in a largely Catholic population.
Puerto Rico is indeed tied to the United States in a way Mexico never has....if we're talking about OTL, where Mexico was never a part of the United States. ATL Mexico is directly annexed by the United States, meaning Statehood unlike Puerto Rico and, more importantly, direct rail connections so as to bind the commerce of the new territories to the rest of the Union and to allow for more readily available communication as well settlement. I'm also not sure where you're getting the idea American Whites won't settle in Mexico, given we have the OTL example of large numbers of Southern Whites living as minorities within the Black Belt of the South. You bring up the differing religion, to which I will retort with the IOTL example of Louisana.
Another big obstacle to significant immigration to the core Mexican territories is yellow fever. In the two years the Mexican war lasted, 13% of the US troops died of disease. That doesn't sound like much, but those rates mean that in about 7 years, half of all US immigrants to the core Mexican territories will be dead. The same death rates would apply to US government administrators and US garrison troops. Mosquitoes weren't identified as the primary yellow fever vector until 1881, this wasn't proven until 1896, and didn't receive widespread acceptance until 1900. The first yellow fever vaccine didn't come into use until 1938.
Undoubtedly disease is an issue, but we once again have the IOTL example of the South. Further, attempting to compare the circumstances of an Army at war, a very unsanitary situation on the whole of itself and one rife with exposure to things like Malaria or Yellow Fever, to one of peacetime conditions isn't a very good comparison.
The Germans were an immigrant community moving into a English-majority nation. They did end up speaking English, but up until World War I a lot of them lived in ethnic German towns or neighborhoods. For many of them, German was their first language, they went to German language schools, they attended German language churches, they read German language books and newspapers printed in the US. Old Order Amish and Old Order Mennonites still live in separate communities where they still speak German.
As DanMcCollum correctly noted, the Mexicans would not be an immigrant community moving into a English-majority nation, the Americans would be an immigrant community moving into a Spanish-majority region.
And just as the Germans, they would end up inevitably assimilated into the majority culture for the most part. As you note, the Germans had their own newspapers, their own communities and indeed often made up the majority in the regions they settled; they still ended up speaking English and adopting to the predominant culture for the most part.
American government structures would replace Mexican government structures, but DanMcCollum was talking about "social and cultural infrastructure", which would not disappear. Even in those parts of Mexico which were annexed in OTL, Hispanics have maintained a distinct cultural identity. In the Mexican core region they would remain the majority, with their own distinct language and culture. That could erode over time, but the American South maintained a distinct dialect and cultural even though they had vastly less difference in language, culture, and religion from the rest of the United States than the differences between the language, culture, and religion of the United States and the language, culture, and religion of Mexico.
That there will be a regional identity in the former Mexico goes without question, but such does not preclude any sort of assimilation to the dominant American culture.
English certainly is the the global lingua franca and it has affected the cultures of former British colonies, but even Ireland, Scotland, and Wales have maintained separate cultural identities, not to mention India, Pakistan, Bangladesh, Egypt, Sudan, Somalia, Kenya, Uganda, Tanzania, Nigeria, Afghanistan, Bahrain, Brunei, Sri Lanka, Hong Kong, Kuwait, Malaysia, Belize, Jamaica, etc
Sure, but no one claims a language alone binds a nation. Attempting to compare, India to Wales or Malaysia to Scotland is an apples to oranges comparison for obvious reasons too.
The US could have built a transcontinental railroad sooner than in OTL, but while the majority favored the central route built in OTL, politicians from the slaveholding states favored a southern route and blocked any attempts to fund a central route. Adding Mexican states may change that balance, but it will make the deadlock worse, so in TTL a transcontinental railroad probably won't be built until at least a decade later than in OTL.
The Pacific Railway surveys found that the Southern route was actually the best, and this was the reasoning behind the Gadsen Purchase. By the time said Purchase was made, however, the sectional divide had reached the point that the deadlock on the matter had arose. Here, without the need for an additional purchase and the sectional divide unlikely to flare up as bad it did in IOTL 1854, the railway will definitely begin construction in the 1850s.
In a 2014 University of Texas/Texas Tribune Poll, 27 percent of registered voters
considered themselves to be Texans first. That's 170 years after Texas was annexed.
So in other words the overwhelming majority of Texans, even in the extremely polarized political environment that exists in our modern day, still place being American first? Exactly as I've been saying, I do believe.
