The piece of art looked like a classic Louis Vuitton steamer trunk. But it opened to expose ... a working toilet. It was part of artist Toland Grinnell's 2002 installation Pied-à-Terre, at New York City's contemporary Mary Boone Gallery, which showcased 34 such retrofitted trunks—including a mink-covered bed, a dog spa, and a pop-up fireplace. "It was inspired by a camping trip we took that made me think about all the stuff people need just to live in a civilized way," he says. The project was the conceptual artist's wink at the lie known as "getting away from it all."

Then, in the summer of 2004, he and his wife, SunHee Grinnell, had a son, Roman. Toland started toting a diaper bag—in many ways, just another version of a portable toilet—and all of a sudden, the joke was on him. "It is absolutely bananas how much stuff you need to get out of the house with a kid," the 38-year-old says. And so began the paroxysm of frustrating bag auditions ("I went through L.L. Bean, Longchamp—you name it, I tried it," SunHee recounts), which eventually led to Mr. B, their collection of nine diaper bags and family-size totes.

Having already created a line of luxury bags in 2002 and 2003, Toland had experience in bag design and production, and SunHee, a magazine editor, had lots of ideas and doodles. "So right from the word go, we were on track to come up with an awesome thing, because SunHee is crazy and I know what I'm doing," he says, laughing. "You can quote me on that. I don't think she would disagree."

Now, two years after those first sketches, Toland sits on a bench in Brooklyn's Prospect Park and offers a demo of Mr. B's Runner diaper bag, while Roman runs back and forth looking for bugs and leaves and delivering acorns. It was in this same spot that Toland conducted guerrilla market research to fine-tune his creations. "I would ambush moms and show them the bag, and sometimes I would have them take one, try it, and tell me how it worked," he says. He points out the focus-group influences: The clip straps attach to a stroller frame but also turn the bag into a hobo purse in a matter of seconds. The flap closure is claspless and Velcro-free. ("I had a mom test one with Velcro, and she told me that the baby woke up when she ripped it open.") Toland refers to these as "small but huge innovations"; perhaps the most notable is the backlash against an excess of interior pockets. "There are so many bags out there with separate pockets for keys and your cell phone, but I kept hearing moms didn't want that," he says. "How helpful is an opaque pocket labeled 'Dirty Duds'?"

For those who prefer lots of pockets, Mr. B offers Spy Bags—durable, clear-vinyl zip-top sacks in different sizes that can nestle inside the Runner or hang from a stroller. "When you're a mom, you're overwhelmed," SunHee says. "But when you have things in order, when you can open your bag and see everything you need without desperately rooting around, you can think, I'm not a bad mom, because I am organized." Then she returns to the word her husband used to describe that camping trip, way back when: "You feel civilized."