Learn Portuguese (Portugal): O diretor quer que vocês vão ao departamento amanhã. - The director wants you to go to the department tomorrow.

It actually is the subjunctive! For the irregular verb ir (to go), the vocês form in the present subjunctive is vão. It happens to look exactly the same as the normal present tense (indicative). We know it is functioning as the subjunctive here because the phrase quer que forces it to be.

What is triggering the subjunctive in this sentence?

The verb quer (wants). When one person (the director) wants someone else (you all) to do something, Portuguese uses que (that) followed by the subjunctive. Expressing a wish, desire, or command for another person is one of the main reasons we use this mood.

Why is it ao departamento and not just a departamento?

The verb ir (to go) requires the preposition a (to) for short trips or visits. Because departamento is a masculine noun, you must combine the preposition a with the masculine word for "the", which is o. Together, a + o contracts into ao.

Is it strictly necessary to include vocês here?

Grammatically, you could drop it and say O diretor quer que vão... However, because vão can mean "you all go" or "they go", leaving the pronoun out might confuse the listener. Keeping vocês makes it completely clear who is supposed to go to the department.