What kind of relationship developed between the U.S. and Mexico after 1821, when Mexico gained independence from Spain?
The relationship that developed between these two countries centered around Texas, where the countries came together at that time.
Just before Mexico became independent, the Spanish had started to invite American settlers to come to Texas. They wanted a larger population for the area and one that would make it economically viable. Texas was far from the populated areas of Mexico and it was easier to find Americans to settle it.
This relationship quickly became a problematic one. More Americans came than the Mexican authorities really wanted. In addition, they refused to keep their promises to assimilate into Mexican ways. When combined with the fact of filibustering expeditions into Texas such as that of James Long, Mexico came to fear that the US had an eye on Texas.
The relationship between the two countries, then, was one where Americans looked down on Mexico to some extent and Mexico feared US domination.