Was their a relationship between the Pre-Columbian cultures of Mexico (the Aztecs, Maya, etc) and the Native American groups of North America? If so, what was the nature of the relationship?
Mexico is part of North America.
There's a huge swash of Mexico north of Mesoamerica, sometimes called "Aridoamerica," that include indigenous groups such as the Huichol, Seri, and others. This region served as a bridge between the American Southwest (Oasisamerica) and Mesoamerica and facilitated trade and cultural exchanges.
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There are artifacts that suggest some trade, but the biggest limit for trade between Meso-American and other aboriginals was the lack of pack animals. Trade was largely dependent upon water ways; this is why the Great Lakes and Mississippi River were such vital conduits of trade (something that continues today). Locate Mexico City on a map, and you'll see that there isn't much in the way of water routes to connect it easily to any other sources of trade. This meant trade was essentially limited to small scale merchants likely trading items from place to place. By this mechanism, an item can go from the shores of the Great Lakes to the halls of Tenochtitlan; it just needs to pass through many different hands to get there. However, in general, it appears the Rio Grande represents the southern limit of trade for most 'Amerindian' products. Both the Hopewell and Cahokia cultures essentially see the import of products stop there, at least from what survives.
That said, there certainly were people making treks back and forth, and we know this because maize spread from its original domestication point, likely in the same neighborhood as the future Aztec Empire, all the way up the Mississippi. Of course, the spreading of a crop (a process that likely took centuries) is a bit different than trading relationships, but the former does suggest that something of the later did exist, at least temporarily.
