The pair have worked together in the past when she directed him in her 2007 short film Cutlass, but being on set with him for the new film reminded her of magical moments when she would visit Kurt and her mum Goldie Hawn while they were filming.
"That was cool," she told U.S. breakfast show Good Morning America on Wednesday. "What I really, really loved about being on set with him was it was a reminder of where I fell in love with making movies."
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"It's a very different experience watching a movie and watching a movie being made because (being on set) is horribly boring," she added. "But, for me as a kid, I loved every aspect of it."
The 37-year-old also appreciated watching Kurt act: "He's such a phenomenal actor," she said. "He would put so much care and effort into his roles in a way which is different with a lot of young people I've worked with. It's such a different mentality."
Kate plays the real-life wife of Mark Wahlberg's oil rig worker Mike Williams in the movie about the Gulf Coast Deepwater Horizon disaster in 2010, when 11 people were killed in an explosion.
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"I literally get the chills every time I talk about it," she said. "(My) character represents all of the families on the Deepwater who were left in the dark for many hours - not knowing what was going on with their families, not having any idea if they were going to come home."
And she felt pressure playing the real-life role because of the emotional toll she knew it would take on the families.
"You have this sort of extra, added thing in the back of your head going, you know, the families are going to see this movie, so you really want to be careful," she continued. "There's no carelessness going into making a film like that when you know that the families are watching."
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