With Kate, 31, resting at her parents' home in Bucklebury, Berkshire, William joined Prince Harry, 28, at a charity polo match in Cirencester Park, Gloucestershire, on Sunday to benefit homeless charity Centrepoint, Child Bereavement UK and WellChild.
Though he was engaged in the match, Kate wasn't far from William's mind – protection officers were on hand to whisk him away to London (by road) should she have gone into labor.
"He is glowing about this wonderful time in his life – and I think we should be glowing with him," Danielle Alexandra, a trustee of Centrepoint, told PEOPLE at the event. "My sense is he's excited and very happy at the chance to be a father. He's one of the most loving people. ... He's a perfect guy to be a dad."
William and Harry's appearance helped raise "substantial" funds for Centrepoint, Chief Executive Seyi Obakin says.
After the game – which they lost – the young royals met formerly homeless people whose welfare has improved because of the charity.
"He wants to understand what the real issues are and listens and talks to them," says trustee Penny Francis. "He's so supportive behind-the-scenes when he meets young people."
At the beginning of the game, William showed a hint of his fatherly side as he made faces with a little girl perched on the shoulders of her dad.
At one point in the fourth chukka (period), William flicked the ball toward the crowd and over the small board around the pitch. "Oh sorry, sorry," he called out to the startled spectators.
The atmosphere in the quiet patch of English countryside was one of calm anticipation, but there was a noticeably heightened police presence in the area. Locals say that whenever Kate is home with her folks the sleepy village suddenly fills with both marked and unmarked police vehicles.
A local source tells PEOPLE, "Like all new arrivals, everyone is just keeping their fingers crossed that it all goes smoothly and mother and baby will be both fit and healthy. ... It is obviously very exciting that the future King or Queen of England will soon be living in the area."