One day after attending theTrooping the Colour celebrations, Kate and her older two kids,Prince GeorgeandPrincess Charlotte, went to cheer onPrince Williamat hischarity polo matchin 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 sonPrince Louison 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 acasual striped blue sundressfromZarapaired with3-inch espadrille wedges(that she laterran 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 cousinsPeter 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-OldPrincess CharlotteTook 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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Maserati Royal Charity Polo Trophy

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Maserati Royal Charity Polo Trophy

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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.”

source: people.com