I agree with most of your excellent analysis of #1. we can, perhaps, more clearly see the relationships if we replace the indirect object with a prepositional phrase:
Some schools + were denying + an equal opportunity to choose a vocational pathway + to their brightest students.
IF I understand my books correctly, "to choose a vocational pathway" is an adjectival infinitive phrase. That is to say, it modifies the noun phrase "an equal opportunity." Here are some examples from one of my favorite books:
His attempt to fly.
A trap to catch the thief.
Nothing to do.
Source: House and Harman Descriptive English Grammar (1950).