How do I potty-train this stubborn 5 month old puppy?

We've had her since she was 5 weeks old, and these past several months have been anything but bliss. I've raised, fostered, and cared for many dogs in my 15 years as a pet owner (aside from childhood pets), and NEVER had such a problem potty training a puppy! She pees outside, but refuses to poop outside, no matter how long she stays out there. She'll come back in and, within minutes, find some hidden place to poop. Her current favorite place to poop is in the laundry room. I'm pretty diligent about taking her outside, and I take her out about 5 times a day, but with 3 young children, I can't follow her around every waking moment. This puppy has me at my wits end day after day since we've had her. I've grown to resent her, and absolutely have no idea what to do now. Why won't she poop outdoors?!