"It makes it much more fun," Russell told ET about working with Hudson. "Last night, we were out until the wee hours, and it's fun when you're with your daughter and you're having a good time."
Hudson was equally glad for the quality one-on-one time.
"It's just a nice moment for us to spend some real time together, and have conversations without being interrupted by one of my millions of brothers," Hudson said. "It's like I have my daddy all to myself. It's kind of nice."
Russell helped raise Kate and her brother Oliver after their biological father, Bill Hudson, split from their mom Goldie Hawn in 1982. Russell and Hawn have been partners since 1983.
"I spent a lot of my childhood on sets, visiting my parents," Hudson said. "Being on a set with [Russell] again for consecutive days reminded me so much of being a kid and falling in love with being on sets."
In the film, Hudson plays the wife of an oil rig worker played by Mark Wahlberg. The movie, inspired by the oil rig explosion in the Gulf of Mexico that took place on April 20, 2010, honors the brave men and women whose heroism saved many on board during the world's largest man-made disaster.
Deepwater Horizon, also starring John Malkovich and Gina Rodriguez, hits theaters Sept. 30.