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George and Amal Clooney’s summer vacation in Italy has all the familiar hallmarks of their go-to July getaways: sun-kissed downtime at their villa on Lake Como and laughter-filled pasta dinners with friends.

This time, however, there are two newcomers on the la dolce vita scene: Ella and Alexander, the couple’s 7-week-old twins. And the new parents are relishing every moment.

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“George and Amal are very hands-on,” a source tells PEOPLE in this week’s issue. “The babies keep them very busy, but they both seem to love being parents.”

“The weather has been fantastic — sunny and warm every day,” the source adds. “George and Amal are enjoying the summer with their babies. Both seem very happy.”

While they spend most of their time at the villa with the twins, who were born in London on June 6, and visiting pals — including George’s longtime friend, producer Ben Weiss — the Clooneys have enjoyed a few low-key date nights.

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The two “sat close and cuddled” over a candlelit dinner on July 18 at the Grill in the Villa d’Este Hotel, an onlooker tells PEOPLE.

“George had his arm around Amal for most of the dinner,” the onlooker adds. “They were both in the best mood.”

Of course, there’s no late-night carousing these days. “On the rare occasion they leave to have dinner, they don’t stay out late,” says a source. “It’s like they enjoy having a night out with friends, but the babies are still the main priority.”

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After dining at Il Gatto Nero, a favorite local spot, on July 11, the Clooneys made sure to call it an early night. “In the past they always dined for hours,” says a source.

“This time it was obvious they didn’t want to be out too late.”