How can America avoid mexican- american War, and will this lead to a stronger mexico?

The northern portions of Mexico were sparsely and are just voids waiting to be filled by dedicated settlers. These portions were also neglected by Mexico City, which is one reason there was an independence movement of sorts in California. They favored annexation either by the US or Britain. With all that extra territory I doubt Mexico will be any stronger, but will always be short of funds to properly exploit the area.

It just may end up being a filibusters' paradise.
 
Have the Mexican authorities be very firm in denying slave ownership in the Texas territory. Make it plain that paper trickery would not be tolerated, and that any “Negros” crossing into Mexican territory would automatically and permanently be free citizens.

Mexico would have to change it's laws to do that. While slavery was technically illegal, it was legal to have 99 year indentured servant contracts, and most of the slaves were brought in under this fiction. Plus, some wealthy families in Mexico had out and out slaves, in the form of Native American house servants (supposedly, they were 'exotic'). Santa Anna make some noise while in TX about freeing the slaves, but he didn't really dare do so while back in Mexico, for fear of angering the wealthy...
 
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