Final answer:
Emperors Nero and Caligula were notorious for squandering wealth on luxuries and scandalizing Rome with undignified public displays, including engaging in activities reserved for low-status individuals and acts of self-glorification that opposed Roman family values.
Step-by-step explanation:
The two Roman emperors who were notably infamous for their extravagant expenditures and scandalous public displays were Nero and Caligula. These emperors are known for their violation of traditional Roman values, which greatly offended the sensibilities of the elite Roman society. Nero is reported to have diverged from Roman norms by styling his hair in an unfamiliar fashion and engaging in lavish public entertainments. On the other hand, Caligula's rule was marked by acts of cruelty, megalomania, and excessive spending on displays of power, including replacing the heads of statues of gods with his own and appointing his horse as a consul.
Their actions, which included public performances in roles traditionally seen as undignified for people of high status, and wasteful spending on grand entertainments and personal glorification, caused disdain amongst the senatorial and equestrian orders, as well as the general populace. Such behavior was contrary to the Roman family values held at the time and contributed to the negative legacy they left as leaders of the Roman Empire, as described by historians and biographers like Suetonius.