The term that is defined as “a legal doctrine that permitted racial segregation in public facilities" would be "Jim Crow", which was a series of such laws passed in the South after the Civil War.
A key factor that pushed Mexicans to emigrate was not being able to support themselves at home, politics also affected them.
The Treaty of Paris of 1763 ended the French and Indian War/Seven Years' War between Great Britain and France, as well as their respective allies. In the terms of the treaty, France gave up all its territories in mainland North America, effectively ending any foreign military threat to the British colonies there.
Left people with the inability to purchase essential goods, such as food.