Learn Italian: Volevamo partire, ma abbiamo dovuto disdire tutto per un'urgenza. - We wanted to leave, but we had to cancel everything due to an urgency.

This is the core of how past-tense modals work! Volevamo describes an ongoing past intention or state of mind (we wanted to leave, but the action wasn't completed). Abbiamo dovuto is a sudden, completed action (we were forced to cancel, and we actually did it).

What if we had used the imperfetto for both, saying dovevamo disdire?

If you say dovevamo disdire, it means 'we were supposed to cancel' (an ongoing obligation), but it leaves it a mystery whether you actually did it or not. Using the passato prossimo (abbiamo dovuto disdire) confirms that the cancellation definitely happened.

Why does dovere use avere as its helper verb here (abbiamo dovuto) instead of essere?

In the passato prossimo, modal verbs usually 'borrow' the helper verb of the infinitive that follows them. Because disdire (to cancel) takes avere, the modal verb jumping in front of it must also take avere. If the action we had to do was a verb taking essere, like partire, it would be siamo dovuti partire.

Why use per in per un'urgenza? Doesn't per mean 'for'?