Complex sentence: From this palace's balcony, Iturbide accepted the offer to be Mexico's first emperor after independence from Spain and during his reign (1821--1823) this house served as the royal palace.
Split into simpler sentences: From this palace's balcony, Iturbide accepted the offer to be Mexico's first emperor after independence from Spain. During his reign (1821--1823), he lived here, using the house as the royal palace.