Kim Lopez has been a teacher for more than two decades. But as the wife of an Air Force service member, she struggles to maintain her career because of the complex requirements for out-of-state teaching licenses to be recognized. Mrs. Lopez has active licenses in California and Virginia, but she’s relocated nine times and has had to fight through red tape with each move.

When Mrs. Lopez and her husband moved to Utah in 2017, she discovered that she would have to retake several exams and spend more than $700 to transfer her...