Learn Portuguese (Portugal): O duque fez-lhe usar a coroa.

This is the core rule for causative verbs like fazer (to make or cause). When the second verb (usar) has its own direct object (a coroa), the person being forced to do the action (the causee) must be an indirect object, so we use the dative pronoun -lhe. If the second verb didn't have a direct object (for example, 'The duke made her leave'), we would use the accusative direct object pronoun -a (O duque fê-la sair).

Could we attach the pronoun to the infinitive instead and say O duque fez usar-lhe a coroa?

No. With causative verbs like fazer and deixar (to let), the pronoun representing the person doing the action must attach to the conjugated causative verb (fez), not the infinitive (usar).

Since -lhe can mean 'him', 'her', or formal 'you', how do we know it means 'her' in this sentence?

Out of context, we don't! The sentence O duque fez-lhe usar a coroa could equally mean 'The duke made him wear the crown' or 'The duke made you wear the crown'. The translation provides 'her' based on an assumed wider context.

Why is usar translated as 'wear' here? Doesn't it mean 'use'?