When Chiara Monti went to her office on Monday morning, she joined millions of Italians returning to work after nearly two months of being on lockdown because of the coronavirus. And when she arrived, she immediately went to the personnel office and asked to have her hours reduced.

Like many working parents, Ms. Monti faced a dilemma: how to ease back into her professional life when her three young children still can’t go to school. Italy, once the epicenter of the coronavirus outbreak in Europe, became the first European country to impose national lockdown restrictions on March 10.