"The best part is my parents," Parker, 44, told PEOPLE at Saturday's Los Angeles Confidential pre-Emmy party, which she hosted. "I get to call them if they don't know already, but usually they know before me. That's absolutely the best part."
Parker – who is up against Tina Fey, Julia Louis-Dreyfus, Christina Applegate and America Ferrera for comedy actress in a series – has been nominated twice for Weeds. She won an Emmy in 2004 for the miniseries Angels in America – and can sometimes feel pressured to keep scoring nominations, she told PEOPLE.
"You kind of feel that if you don't get nominated, you're letting people down a little bit," she says.
Her Kids Are FansParker's two children, William, 4, and Caroline, 1, will be watching at home and they are among her biggest fans. Parker adopted Caroline last year, while actor Billy Crudup is the father to William.
"It's just extremely humbling," Parker says about motherhood. "They do [get along with each other]. They're incredible together. They're super sweet!"
Parker's Weeds costar, Kevin Nealon, joked at the party that he's got Parker in his thoughts for Sunday's Emmys.
"I haven't seen her since we taped the last episode, but spiritually I've been sending her good vibes," Nealon says. "I don't know if she's received them, with the airwaves today so crowded."