Decolonization still there, but Mexico can always find a better way to reform its empire into a similar system like the Commonwealth's Westminster System, where the head of state is the monarch but each nations was granted independence and had their own economy, military and goverment. Surely it will lose some colonies later on but in the end, the Multi-national Commonwealth System is definitely worth trying for reforming the Empire into a true democratic entity in Post-War era.
Reasons why it still can happen:
-Bankruptcy, both the Germans and Mexico were exhausted after the war and with colonies becoming more and more expensive to maintain and keeping control, the best way is to grant them independence to save yourself the troubles of governing them.You really cant keep them forever in the long run.
-New wave of progressive democracy ideologies from the US as well as the inspirations for nationalism that the Axis sorta gave them. The Axis ideologies are bad but their noble causes for supporting colonial independence movements are appreciated. This happens OTL with Indonesia
-The US economy now had outgrown other Great Powers in the aftermath, as many of them were still recovering from the war, the US emerged largely unscathed, and furthermore, they were pretty keen on supporting decolonization as well, and they would set off the first example by granting Philippines independence.
-The Ottoman Empire is also weakened badly in the aftermath of the war, so granting indepedence to the Balkan states might save them from the headaches of ethnic nationalism and its powder keg. For the Arab problem, i really dont know as if they let the local Arab rulers to rule their own lands, this might lead to the rise of sectarian Wahabbism so its might be a No-No as the Empire itself is pretty much quite secular and westernized at this point to be sullied by radical Muslim in the Middle East.
For the Post-WW2 cold war, its gonna be between the Monarchism and Republicanism between the German Empire and the United States. The Mexican Empire however, leads the Unaligned Movement as they had many of their allies both as democratic republics (like Ireland) and constitutional monarchies (like Poland). Other than that, my guess for the Danubian Empire is that it might broke up like the Soviet Union OTL due to ethnic nationalism problems and each nations choose to vote its own referendums to stay or leave in a much more peaceful way.
Also, German Empire would have proposed their own continental alliance equivalent to European Union in Post-War era, although how big this alliance is gonna be is up to you to imagine, one thing for sure, it might include the Ottoman Empire in as they had proved themselves to be quite adept at it.
The United States, Dominion of Canada and Second Mexican Empire later on could form their own EU equivalent, the North American Union as their shared economic/political alliance in the post-war period. Although the leader of this union would be rotated around, with representatives from each nation held the position each year instead of having a definite powerhouse leading them as all the three nations are militarily capable and had well-developed economy ITTL.
The rising powerhouses of Post-War era ITTL are likely going to be: China, Second Kingdom of Italy, Dominion of Canada, Commonwealth of Australia and New Zealand, Japan, India.
One thing however, the Dominion of Canada would become part of the new United Kingdom of Great Britain and Canada in the post war, in a similar fashion to Austria-Hungary, the Dominion of Canada would still retain its own government, economy, but their military is the same as the British military in post-war era. The UK would also had two overseas capital of their own, Ottawa and London, while the power of the British Colonial Empire had diminished, the economic boom of the Dominion of Canada, largely untouched by the war improved significantly thanks to the establishment of the Royal government in exile and the massive rapid pre-war industrialization efforts in preparations for retaking their Home Islands.
In the end, losing Ireland perhaps isnt too bad afterall, they gained Canada as part of their new pluricontinental United Kingdom, just like what the former Brazil-Portugal once was. Although for the case of British Commonwealth, things went much smoother and both nations gladly accepted their union as equal sovereign nations, just like the rest of the nations within the Commonwealth like Australia, New Zealand and Hong Kong Protectorate.
Also, for a new flag of Post-War Mexican Commonwealth, i suggest we using this, its a way to remember the legacy of the old Spanish Empire as well as the legacy of the Habsburg through the Cross of Burgundy symbolism.