No, rather I want a Timeline where America gets none of Nuevo Mexico or Alta California, only the lands controlled by the republic of Texas
You might want to consider a POD where the US does much worse in the War of 1812. That might mess up the Louisiana purchase and Texas, but the challenge, is that by the time the US annexes Texas, the broad strokes of history are going to be hard to butterfly away.
Another option is one in which the US has more pronounced internal divisions than IOTL, where the energy needed to have settlers claiming new territory is stymied.
But here's an idea. Say that Aaron Burr is actually successful in his effort to colonize Texas and he manages to split off Texas from Spain during the height of the Napoleonic Wars by means of payment or something along those lines. After the Spanish Empire implodes and Mexico's revolution is launched, Burr's little republic manages to make a claim of independence stick. The war of 1812 fires off, but goes worse, and Britain ends up holding New Orleans after the treaty of Ghent is signed. The US and UK spend the next 20 years negotiating shipping rights along the Mississippi, causing places like Arkansas and Missouri to lag well behind their OTL rate of development.
In this scenario, Burr dies in 1836 like IOTL, but his death results in a shift in thinking in his little rump republic and his successors appeal to the US for annexation.
I'm sure there are plenty of holes in this but it seems to me to be one way to have things sputter out after a Texas annexation.