The Second Mexican Empire after the First World War was at the Zenith of it's power, it had control of Southeast Africa, the entire Horn of Africa, South Africa, Rhodesia, Indochina, India, it now dominated the Caribbean with Jamaica and the Bahamas. Not to mention it had client states in The Republic of Ireland and The Kingdoms of Poland and Portugal.
But the main problems Mexico was going through were social, women wanted the right to vote, how to compensate veterans from the war, the poverty of the indigenous people in the south of Mexico, and finally trying to assimilate the English speaking people of Belize.
This is how people voted in the 1920 Mexican elections for Prime Minister between the Conservative party's candidate, Francisco Villa and the new Reformist Party's candidate, Emiliano Zapata (Zapata was a hero for his continued resistance against both British and Italian forces during the Somiliand front.)
In December 1, the Reformist Party won a surprising landslide and Emiliano Zapata was now Prime Minister, this was a major upset because not since the start of the Empire, the Conservatives had always won elections.

Prime Minister Zapata
Zapata's first act as Prime Minister was to compensate veterans by giving them land in the North and money to support themselves until the harvests, this would satisfy veterans until in 1929.
The next deal was to help the indigenous people by funding more schools and giving more modern equipment to the poor farmers and campesinos. As for assimilating Belize he took a hard stance on English speaking people, it was now punishable with a fine of 50 Pesos to be speaking English in public, while this was repealed it nonetheless caused a exodus of English people who still lived in Belize and many fled to either Brazilian Guiana, where they were much more lenient on English or they went to the United Kingdom in exile in Canada.
As for the military, the Imperial Mexican Army was still kept at it's maximum of 100,000 soldiers in the North because of the recent arming in the US southern States. For the colonies, it was mandatory for every colony to have a maximum of 20,000 troops to keep the colonies from revolting, but after the 1918-19 Rebellions, no new Rebellions spring out, so the colonial forces were minimize to just 10,000 in 1926.
The Navy was at first downsized and spending was cut to fund building and social projects. That was until in November 13, 1921 when the Japanese unveiled it's first aircraft carrier,
Hōnshō, the first aircraft carrier of the world.
Hōnshō
Realizing they now have competition in the Pacific and worst the Japanese could threaten again the Mexican colonies, especially the Crown Jewel of the Asian colonies: Indochina, Prime Minister Zapata focus all spending on the Navy with Zapata quoted as saying
"Every last Peso, Silver, Gold, and Diamond piece will be used to not let them end Rule Mexicania."
The first Mexican aircraft carrier was the
BSM Virgin de Guadalupe, revealed in February 4, 1922 the first of her kind.
BSM Virgin de Guadalupe
This began a new arms race with the Aztec eagle of Mexico vs the Rising Sun of Japan, by the end of 20s the Mexican and Japanese navies were the first rate of the Pacific, with both having the same number of Battleships: Mexico 20, Japan 22. in aircraft carriers: Mexico 23, Japan 25. Armoured cruisers: Mexico 20, Japan 18. Destroyers: Mexico 170, Japan 169. The only field Japan beats Mexico in was in Submarines with Japan having nearly 200 compared to Mexico's 50.
The Pacific Arms race would continue until 1929 with the advent of the Great Depression and the two empires would enter into a agreement in 1930 In the Buenos Aires Agreement to no longer 1-up each other and to let each empire have their own spheres of influence: Mexico: Southeast Asia and India Japan: China, Korea, and Mongolia.
The agreement was signed between the Naval commanders of the two nations; Japan's Tōgō Heihachirō and Mexico's Hilario Rodriguez Malpica Segovia in September 1930.

Tōgō Heihachirō
This didn't stop the Mexican Japanese enmity with both using the Warlords in China to poke at each other. Back in 1925 Mexico was supporting greatly the Fengtian clique and Beiyang Government in Manchuria, which was considered by Japan it's sphere of influence and it was because of Mexican support to the Warlord Zhang Zuolin, with them providing Rifles, ammo, canons and advisors that the Northern Expedition ended in disaster. Because of this Japan began supporting the Kuomintang Government in Nanjing.
Even after the Buenos Aires Agreement this didn't stop the proxy wars.

Warlord Zhang Zuolin

Mexican racism

Japanese samurai smashing Mexican ships
(I couldn't find better one to convey the point of Japanese Mexican rivalry.)
In Mexico, the middle class began to boom with wealth coming from the reparations from Britain and France and because of this the Mexican stock market boomed with many investing. Women were finally given the right to vote in 1927.

the Locos años veinte
However the greatest crisis began in 1926 when Agustín II passed away and Emiliano succeeded him, but he was 14 years old and a Regency was made with his mother Stephanie and Prime Minister Zapata. But the real crisis began in 1936 when the now crowned Emperor Emiliano I was supposed to marry his arranged fiancee Ileana of Romania, however he proposed to the Infanta of Spain, Princess Beatriz of Spain, daughter of Alfonso XIII, whom he been going out with and had more in common with than his arranged bride.
This was unacceptable and the Government was split with conservatives backing the Romanian Princess called "Rumanistas and the Reformists backing the Spanish Princess called "Peninsulares". The Conservatives wanted the marriage with Ileana to strengthen ties with Germany's Hohenzollern dynasty while the Reformists saw a alliance with Spain more beneficial with Spanish Malaya as a base to station the Marina Imperial's Pacific Fleet.

Infanta Beatriz of Spain
Zapata was at first supportive of the Emperor until he needed conservative support to push bills through to help mitigate the Depression and so told the Emperor that he must marry Ileana. The Emperor refused and threaten to abdicate, now things got heated. Realizing that if he abdicates then that would leave his more liberal sister Isabel Marie, now Queen of Poland, the Conservatives in no way wanted that and so on May, they finally caved in. In May 12, Emiliano I and Beatriz married, making a possible Uníon between Mexico and Spain possible. For the following two more years things were peaceful until the Union of Britain and Vichy France declared war on Spain and Germany dragging Mexico in the Second World War.