Last summer, Tyler Haney, the founder and chief executive of Outdoor Voices, appeared to be golden.

In just five years, the Instagram-friendly athletic apparel company that she created in her 20s had become a sensation. There was more than $50 million in funding, nine stores and appearances on the business conference circuit. A glowing profile in The New Yorker had anointed Outdoor Voices the next Lululemon. In July, Ms. Haney shared the news that she was pregnant on “Good Morning America” with an enthusiastic message about work, family and having it all.

But behind the scenes, Outdoor Voices was cracking.

Store openings were delayed after leases were signed. A string of experienced executives, hired to professionalize the start-up, had abruptly left. An anonymous letter sent to the board of directors blamed Ms. Haney, now 31, for the exits and accused her of being “spoiled” and mercurial. The clothes were selling at discounts. The office in New York, where Outdoor Voices was based before it moved to Austin, Texas, would soon be shut down.

And a schism had opened between Ms. Haney and Mickey Drexler, the retail legend heralded for his leadership of Gap and J.Crew, who gave Outdoor Voices a halo of can’t-fail credibility when he became an investor and its chairman in 2017.

Mr. Drexler’s decades of experience and deep knowledge of the retail industry were expected to help Outdoor Voices make the transition from scrappy start-up to mature business. But his input was not always welcomed at a company built on the vision of its charismatic founder.