Mexico is not much different from other Latin American countries really. Yes there was foreign meddling but a country like Bolivia manages to have some sort of world record of coups (200 in 200 years) overwhelmingly if not exclusively a domestic product. The gunboat intervention by the Europeans left no real institutional mark on Mexico, the constitution remained the same. In terms of South America, Uruguay is doing the best by far, and its colonial context was cattle, trade and European settlers - few natives to coerce and exploit, no slave plantations set up. There was slave trade and slaves present, but these were domestic/urban labourers and many got freedom fighting for the country before slavery was abolished. Mexico on the other hand had an enormous coerced labour system with elites at the top extracting wealth for themselves.
In your scenario I assume the north remains free. The CSA would have been another Mexico or South Africa on its own. The north could use their restore union casus belli at an opportune moment afterwards, it was already wealthier and more powerful than the south, that divide would only grow starker as separate countries.