Almost the same thing happen in my own game with only slight differences.
- USSR simply doesn't care and if "Division Cuba" is involved in Mexico it's only because they couldn't be withdrawn (in my case from Venezuela).
- When Cuba gets involved it's very late in the war and it is as an ally to Mexico, Nicaragua and Venezuela.
- Mexico never fell to communism but only to socialism. In addition it doesn't invade US but it is invaded by a weak US task force sent in to help US refugees because of false allegation of mistreatment by the Mexican authorities. Why would any Mexican flee to USA, a land that is facing devastation?
- Nuking are limited and used only on a few cities (Managua, Maracaibo, Caracas, Havana...) when things start to turn sour for US.
One last point, US doesn't invade Mexico for any greedy reason. All this results only from general chaos added to distrust and misinformation. Then, it is a fairly short campaign ending in confusion for all sides.
An important difference on my side concerns Alaska. The Russian troops there are effectively cut from their homeland but this is also true for NATO units and civilian. Then, threaten by marauders from all sides, they all meet, form an alliance and establish an independent state. This independent Alaska is slightly more socialist but it is fairly supportive of US: civilians are all US citizens, NATO units turn to their allies and the former soviet troops felt betrayed by Moscow.