June 13, 2018 11:35 AM

One day after attending the Trooping the Colour celebrations, Kate and her older two kids, Prince George and Princess Charlotte, went to cheer on Prince William at his charity polo match in Gloucester, England.

“Kate is a fantastic mum,” an onlooker at the match tells PEOPLE. “She was calm with the children.” Using a British phrase for “run loose,” the onlooker says, “She let them have their head.”

The royal mom, 36, who welcomed son Prince Louis on April 23, also used a tried-and-true technique for planning the rest of her day.

At one point, “She seemed to say to [George, 4, and Charlotte, 3], ‘First to the polo field is the winner!’ ” the observer adds. “She was trying to get them tired before they had to get back in the car to leave.”

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Kate watched the kids and rooted for her husband while wearing a casual striped blue sundress from Zara paired with 3-inch espadrille wedges (that she later ran in!).

George and Charlotte also ran around the field and played with their older cousin Savannah Phillips, the 7-year-old daughter of William’s cousins Peter and Autumn Phillips.

“[Savannah] sat with Charlotte in her lap,” says the observer. “She hugged her and balanced her on her knee.”

RELATED VIDEO: How 3-Year-Old Princess Charlotte Took Charge of the Other Kids at the Royal Wedding: ‘No, You Can’t Go Yet!’

Charlotte also took notes from her older cousin as she attempted to do a headstand just like she did, which gave Kate a laugh.

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George didn’t participate in the headstand action, but did entertain himself by playing with a rainbow slinky.

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Despite the photographers, Kate “didn’t get stressed about it, or pass that along to the children,” says the onlooker. “She let them play. She let them get on with it, sliding down the hill and rolling on the grass.”

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