Your challenge, should you choose to accept it, is to have the American Civil War and Mexican-American War happening at the same time. They don't have to start and finish at the same time obviously, but there should be considerable overlap. It doesn't matter whether you're delaying the Mexican-American War or hastening the American Civil War or both.
Secondly, what do you think are the most likely changes from OTL if this happens? Does the US tend to (more than OTL) support independent republics being carved out of Mexican territory and plan to annex these republics as states after the war rather than direct annexation during the war due to its efforts being concentrated elsewhere?