Learn Italian: Siamo stati sfortunati in vacanza.

The prefix s- turns fortunati (lucky) into its exact opposite: unlucky. The s- prefix is very common in Italian for creating negative or opposite meanings, much like the prefix un- in English.

Could I use the prefix in- instead and say infortunati to mean unlucky?

No, and that is a common trap! While in- is another negative prefix, infortunato actually means injured, because it comes from the noun infortunio (an accident or injury). To say unlucky, you must stick with the s- prefix to make sfortunato.

Why do both stati and sfortunati end in -i?

Because they describe the subject we (noi). When you use the helper verb essere (to be) in the past tense, both the past participle (stati) and any adjectives (sfortunati) must agree in gender and number with the subject. The -i ending indicates a masculine or mixed-gender plural group. If the group were entirely female, it would be siamo state sfortunate.

Why is it in vacanza when the English translation says on holiday?

Prepositions rarely translate directly word-for-word. In Italian, the fixed expression for being on a trip or vacation is always in vacanza, never su vacanza. It is best to memorize this as a set phrase.