The United States had argued with Britain and Mexico over which two territories?

Answer 1

I recalled the Louisiana Territory as well as the Northwest Territories as being 'points-of-contention' between the U.S. and Mexico, on one hand, and Britain, on the other hand. Here are two sites for you to read completely to see if my recollections are accurate. I am assuming you are not considering the islands off the coast of Florida that are newer U.S. territories than those listed in the sites below:

https://www.storyboardthat.com/lesson-plans/us-territorial-expansion-1783-1959

U.S. Territorial Expansion (1783-1959) Lesson plans by Richard Cleggett

https://classroom.synonym.com/six-territorial-gains-1800s-23784.html

Six Territorial Gains in the US in the 1800s by Dee Schneiderman