another Map Challenge

Create a TL that includes this map and this information:

-This USA fought a stalemated trench war against Mexico in the late 19th century.
-OTL's Utah is named Deseret and OTL's Nevada is named Utah.
-The USA is in a state of cold war with the British Empire.
-technology, in this world, is roughly ten years behind OTL.
-nukes exist, but only the USA, the British Empire, Mexico, and Germany possess them.

The map is circa 1950. Green is the USA, blue is the British Empire, and the red is Mexico.

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1836 Mexico wins in Texas

The US began to talk openly of the annexation of Cuba – with the support of the big Cuban landowners who didn't want to see slavery abolished. 'There are two dangers to be averted by the event [of annexation]. One, that the island should fall into the hands of Great Britain; the other, that it should be revolutionized by the Negroes.' (John Quincy Adam). He said that Cuba, like a ripe apple, should gravitate naturally to the US if cut off from Spain. In the 1850s, it offered Spain $100 million to buy Cuba, lock, stock and barrel.

1850's US buys Cuba

1876 US Invades Mexico to Restore Juaz to Power
 
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