Eh, just because Mexico could get an European monarch, doesn't mean any of the massive problems that Mexico was facing at the time would go away. The OTL First Empire didn't even exist for two years!
For starters, the Spanish were OTL very much against the Mexicans finally breaking away, so you're going to have to change *how* Mexico becomes free. You could potentially have the Spanish Bourbons flee to Mexico during the Napoleonic wars, and have a similar situation as with the Portuguese and Brazil during this era. Otherwise, unless invoking ASBs, the (Spanish) Bourbons are not going to take the throne of Mexico.
Unless you have a pretty strong conflict going on in Europe, no nation would want to guarantee a war with the Spanish by throwing one of their royals over to Mexico. Plus, I don't know how many royals would be like Max and just hop on over to Mexico, but I'm sure you could find some anyway.
At the opening of the Congress of Mexico, there were three main political groupings, two of which supported the Plan of Iguala, but differed in thinking who should get the Throne (between a Bourbon and Iturbide) and the Republicans. The Republicans supported the Bourbonists, as they were more opposed to Iturbide getting power over a Bourbon. However, when the Spanish declared the Treaty of Córdoba to be null, the Bourbonists broke into the other two parties. After the fall of the Bourbonists, it started to get increasingly tense in Mexico, with Iturbide dissolving the Congress after becoming Emperor due to it criticizing him.
The Mexican economy was in shambles after the struggle of independence, and soon had to cut wages in the military and civil offices, leading to increased desertion and general grumpiness. The treasury was so lacking that Augustin's coronation was with mostly borrowed jewelry. To keep the treasury afloat, forced loans had to happen, and Spanish currency en route back to Spain was seized for the government. (not many liked doing that for some reason) My readings on the First Empire is a little rusty, but I'm nigh certain that several important state mines were in disrepair during this time as well, hindering currency even more. (I really don't remember which book stated that though
)
And the last thing that's in the way of the Empire are several men such as Servando Teresa de Mier, but most importantly, Santa Anna. I don't think I need to get too in depth about it, but Santa Anna was scheming a lot during the time of the Empire. He eventually did get Augustin kicked out ya know.
So what does the Empire need to survive? A few miracles.