Here's a thing.
The position of Prime Minister of Mexico, officially the Presidente del Gobierno de Mexico, is one with a long history. The position was established by the First Mexican Constitution in 1824 as a check on the power of the Emperor, but after the first few Prime Ministers the Emperor decided he didn't really like having his power checked and proceeded to appoint a number of yes-men.
That continued until 1885, when Emperor Felipe ordered the invasion of the United States as a result of 1) the American alliance with Britain, 2) the French alliance with Mexico, and 3) the ongoing conflict in West Africa - though it was really because of 0) Felipe's desire to show off all his shiny new French and German toys. This was, in the most charitable terms, a disaster, and it led to the Second Mexican Constitution, which massively checked the powers of the Emperor. However, this led to only modest gains in power for the Prime Ministership, as most of the executive power went to the President.
Pedro Ñuñez changed all that. The son of a Chihuahuan cowherd, he had the good fortune to become leader of the Partido Socialista right before the Great Panic of 1900, and then successfully rode the wave of popular anger to the head of Congress. Successfully convincing Emperor Salvador I and President Joaquin Ramirez to grant him emergency power, he saw Mexico rise from the ashes to become an economic power with bona-fide colonies (just Cuba and Guam, actually, but still) before his untimely death in 1917. His successors largely maintained that power, although lately the heads of powerful government departments like Secretary of State for the Interior Dionisio Marquez have begun to be seen as "powers behind the throne", as it were.
The current holder, Emiliano Alvarez, is the head of the Partido Conservador, or, as many call it, the Escoseses. A former prosecuting attorney noted for fighting corruption, Alvarez has thus far spent most of his tenure making sweeping cuts to spending, especially the military, and trying to end the last few price controls on consumer goods still extant. As a result, he is a polarizing figure, and has been in a public feud with the more hawkish Emperor, though he has something of a rapport with President Andrés Patil. Rumor has it that Chapultepec is considering invoking Article IX to call for elections within the year, a gamble which may well backfire.
As for the uniform, Prime Ministers customarily wear dress uniforms while in Congress, a practice not obeyed by Daniel Villar, Alvarez's predecessor, but brought back by Alvarez to appease traditionalists.