"They kind of thought there'd be big semi-trucks pulling up to the house on a weekly basis," she says.
An understandable mistake for the kids-8, 13 and 15 years old-since Mom was named senior VP-marketing at Toys "R" Us.
But her job at the toy retailer hasn't disappointed observers, who see Ms. Parker as an effective leader for the retailer's efforts. They point out she'll have a tough fight in the face of price competition from discounters, such as Wal-Mart Stores and Target Stores, that have already driven rivals KB Toys and FAO Schwarz into bankruptcy. Toys "R" Us has fought back with exclusive products, such as the Cabbage Patch Kids revival, and with improvements in stores.
Ms. Parker, 46, didn't set out to be a retailer, but as she tells it, she evolved into one by a series of lucky developments.
As an MBA graduate at the University of Iowa, she'd wanted to be an investment manager but ended up as a corporate financial analyst. While at Yum! Brands' Taco Bell unit, she worked closely with the fast-feeder's marketing department and became interested in their work, so when an opening became available, she decided to try it.
After leaving Taco Bell, where Ms. Parker rose to director of strategic marketing, she followed with stints at several retailers, including grocer Smart & Final, convenience store chain Tops Markets and the Michaels Stores arts and crafts chain.
"I kind of figured I'd work my way out of the food chain," she jokes.
But seriously, moving from fast-food to retail wasn't all that difficult, Ms. Parker says.
"The difference is learning the merchant culture," she says. "The sense of urgency, the adrenaline rush of `Right now' is pretty much the same."
And right now, Ms. Parker is concentrating on the transition to a new ad agency. As part of its attempts to jump-start sales, Toys "R" Us last month moved creative for its $100 million-plus account to WPP Group's Young & Rubicam, New York, from Publicis Groupe's Leo Burnett USA, Chicago.
As for her kids' "delight" factor, they're enjoying some perks from Mom's job, after all.
"I bring them along when I go on store visits," Ms. Parker says.