The Transportation Department said that it received around 30,000 complaints about airline refunds during the pandemic.
"I showed [the necessary documents] to them multiple times, I asked for a supervisor, and at the end of it all they still did not allow us to board," mother Chrystal Becker recalled.
Employees who are not fully vaccinated by October 30 could lose their jobs unless they have "valid reasons" they cannot be, the airline said.
Fatima Abdelrahman described how she as "scared" and "worried" after airline staff allegedly asked her to take off religious headscarf in public.
The passenger recalled panicking, eventually searching for a flashlight to help her open the plane's doors.
Emergency services responded to the scene but the extent of the woman's injuries are unknown.
The flight, headed to Toronto, detoured in Calgary.
Local media reported it was snowing heavily at the airport at the time of the accident.