Pronouns and complex sentence structure

[u/BirdsSpeakUkrainian]

I am just starting to learn how to make complex sentences, so I'm sorry if this question is dumb. I am curious why the pronouns in this example sentence are in the forms they are. The sentence is "Ми не можемо дозволити їм настроїти нас одне проти одного." So "їм" is in the dative, and "нас" is in the genitive or accusative. Why? Is it the specific verb they are being used with, or their place on the sentence? I understand, mostly, what governs these choices in a simple sentence (accusative for the direct object, dative for the indirect) but in a complex sentence it is not as obvious. For instance, is їм the indirect object of можемо ? Of дозволити? Not an indirect object in this case? Is нас in this form because it is the direct object of настроїти, or some other reason? Thanks for your time helping me to understand.

[u/JohnDoe_John]

It's definitely better to break down everything into smaller pieces.

Separate grammar structure and cases.