Learn Italian: Vorrei vedere le ragazze recitare in quel teatro. - I would like to see the girls perform in that theater.

With perception verbs like vedere (to see) and sentire (to hear), Italian uses the infinitive for the action being perceived. This works exactly like English: 'to see the girls perform' translates directly to vedere le ragazze recitare. You do not need a connecting word like che.

Could I change the word order to vedere recitare le ragazze?

Yes, absolutely. With perception verbs plus an infinitive, you can either put the object noun between the two verbs (vedere le ragazze recitare) or put the object noun after both verbs (vedere recitare le ragazze). Both are perfectly natural in Italian.

I learned that recitare means 'to recite'. Why is it translated as 'perform'?

In Italian, recitare is the standard verb used for acting in a play or a movie. So in the context of a theater (teatro), it means 'to act' or 'to perform' a role, rather than just reading lines out loud.

As a quick refresher, why is it quel teatro and not quello teatro?