So your POD is the death of Alvarado followed by a secondary POD combining suppression and appeasement of the Mexica nobility?
Nice start!
Result?
You could have Captain-General Hernan Cortes pick someone other than Pedro Alvarado in garrisoning Tenochtitlan? Anyone would be better than him. And you're not going to have much luck appeasing the Mexican nobility. Cortes failed to get much support though I reckon that was mostly of Alvarado's doing mixed in with holding their Great Speaker hostage against his will. Then again, the nobles were not going to follow Montezuma if he remains a puppet.
Cuauhtemoc is a far more younger, competent and charismatic leader who would lead the insurrection against Montezuma (and what nobles decide to stick with him) and the Spaniards regardless. And he'll massacre the Spanish garrison and see to it that Cortes receives a ghastly end as a sacrifice to the War God.
The way that Savoy handled it in Two Lucky Princes is probably the most feasible way for a pro-Spanish Mexica Empire to exist.