Corrine Hendrickson understands how difficult it can be to find quality childcare. Fourteen years ago, she was working as a retail manager and trying to juggle care for her 10-month-old son with her and her husband's schedules.

One evening, she was talking with three friends, each of them pregnant and struggling to find childcare. Hendrickson asked her friends if she quit her job and used her degree, would they bring their children to her? Soon, Hendrickson was taking care of two babies, born just a week apart, in addition to her own son, and added a third baby two months later.

Hendrick...