07/08/2010 at 01:55 PM EDT
Actress Ally Sheedy is "relieved" and "glad" that she and her 16-year-old daughter Rebecca don't share the same fondness for acting. But there's at least one thing they do share: an affection for animals.
They used to keep a pet rat in their home and more recently adopted a unique canine named Sky. "The rat died. We have a greyhound [now]," the 48-year-old Brat Packer explained at the Life During Wartime
premiere in New York City on July 7. Sky is a rescue dog with a colorful past: the greyhound used to be a racing dog.
"He's got some issues," she said, detailing how his aggressive behavior concerns her. "He's wacky, but when he sees a little dog there's something a little bit scary about that interaction."
Sheedy thinks little creatures may stir memories of Sky's racetrack past. "I think he thinks it's a rabbit," she said, "so he doesn't get to play in playgroups very much."
The actress seems quite happy about her life with Sky and daughter Rebecca – she walked the red carpet to chat with reporters but didn't stay for the movie screening at the IFC Center on Wednesday. "I'm going home," she said, "to be with my child." See more celebrity pets on PEOPLEPets.com:Nick Cannon and Mariah Carey's Pups Love to Doggie PaddleTrista Sutter: My Son's First Word Was 'Dog'