Oliver Hudson was pulling for a cameo in Running Point but didn't quite make the cut. The new Netflix series sees Kate Hudson take the helm of her family's L.A. basketball team, the Waves, while navigating a chaotic sibling dynamic with her scheming brothers Sandy (Drew Tarver), Ness (Scott MacArthur) and Cam (Justin Theroux). Luckily, Kate, 45, had plenty of real-life experiences to pull from as she stepped into the role. "Oh my God, we have such a crazy sibling dynamic," she tells PEOPLE of her relationship with Oliver, 48. "We have a whole podcast about it!" She also reveals that her older brother is "still mad he's not in the show," which prompts creator Mindy Kaling to jump in and say that Oliver "will be" making an appearance — someday. Kate then jokes that her brother could play a "dead body" just to get him onscreen, and when Kaling suggests he'd be "annoyed" with that role, Kate reveals he's game for anything. "He would love it," she says of Oliver. "He'd do it. He would do it." All jokes aside, Kate reflects candidly on how important her siblings are in her life — including brother Wyatt Russell, who their mom Goldie Hawn welcomed with husband Kurt Russell. "Sibling dynamics are really challenging. And you realize — which I love, because I really have spent so many years now talking about it — [siblings] know each other better than anyone. And every good, bad, and ugly thing that happens in your life, it comes out in that dynamic," she says. "But at the same time, when you have them on your side and you choose to work through things together — there's no other bond like it." Getting to play with the "comedic side" of sibling relationships in Running Point was particularly fun for her and "so close to my heart," she says. The banter also came very easily to her and her costars. "Honestly, the chemistry between me and Drew and Justin and Scotty was immediate. It was really interesting," she says. "They were immediately so naughty with me. I'm like, 'You realize we did just have an entire HR Zoom?'" Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer​​, from celebrity news to compelling human interest stories. Running Point is now streaming on Netflix.