What is the relationship between the Catholic churches of various countries?

The Roman Catholic Church, both in the United States and in Mexico, is led by the Pope. The current Pope is Pope Benedict XVI.

The Roman Catholic Church defines its mission as spreading the gospel of Jesus Christ, administering the sacraments, and exercising charity.

Individual countries, regions, or major cities are served by local particular churches known as dioceses or eparchies, each overseen by a Catholic bishop. Each diocese is united with one of the worldwide "sui iuris" particular churches, such as the Latin Church, or one of the many Eastern Catholic Churches. As of 2008, the Catholic Church (both East and West) comprised 2,795 dioceses. The bishops in a particular country or region are often organized into an episcopal conference, which aids in maintaining a uniform style of worship and co-ordination of social justice programs within the areas served by member bishops.

Dioceses are further divided into numerous individual communities called parishes, each staffed by one or more priests, deacons, and/or lay ecclesial ministers. Parishes are responsible for the day to day celebration of the sacraments and pastoral care of the Catholic laity.

Now, as you've observed, any particular Roman Catholic Church parish will emphasize one of the three missions. Either the congregation will follow the lead of the local Priest, or the local Priest will follow the lead of the congregation. In the United States, in general, congregations lead. In Mexico, in general, Priests lead.

Edited to add: What I mean by lead in the previous paragraph is that United States Catholic congregants will quit going to church if the Priest tries to stray too far from what the congregation wants. Unless there's only one Catholic church in town, congregants have choices. In Mexico, because of the culture, it's not as easy to change churches. Therefore, the Priest is given more latitude by the congregants.

Again, as you observed, the Priests in Mexico thought differently about exercising charity than the Priests in the United States. Part of the reason is culture, and part of the reason is who leads, as I mentioned in the previous 2 paragraphs.

Countries or regions each have their own bishops conference.

Conferencia del Episcopado Mexicano

United States Conference of Catholic Bishops

But that is as much as they differ. A bishop, acting as a successor of the apostles (like James as Bishop of Jerusalem) is the leader of his diocese. Then the priest is the leader of his congregation and establishes the norms for conduct within his parish (i.e. if he doesn't want a bible study to be held there, then there shouldn't be a bible study held there).

To your anecdote, I'm not a canon law expert, but it strikes me as odd if it were a priest telling someone that they're excommunicated. He may tell them to take a hike, but I don't believe that he has authority to excommunicate someone. There are offenses, like abortion or helping someone get/perform an abortion that are in themselves automatic excommunication, but what you're describing sounds like disobedience which would require a Bishop's intervention.

In my diocese, we had a similar thing happen with a Religious Ed. teacher who refused to deny things she had written in her master's thesis which were contrary to Catholic Teaching. To my knowledge, she wasn't even excommunicated for that, just fired (you can read more info than you'd ever want here, but I think it should clarify a few things about the way a diocese is governed).

What Gilbert wrote is perhaps the way things look, but in truth, it is not the congregation who leads things in their parish. Throughout the Universal Church, priests are the heads of their parishes.

In the documents of Vatican II, the Church provided for additional lay leadership from within the parish in establishing ministries and financial councils but not complete authority and those documents cover the entire Church, not just Mexico or the United States.