Cassie Hutchins says she feared the worst during a recent United Airlines flight from Denver, Colorado.

Hutchins, 23, was preparing to board a flight to Sacramento on Sunday when, she says, an agent at the gate began to question her about her 8-month-old daughter, Mila.

“He asked about her having to eat, if I was taking her car seat, and where we were sitting on the plane,” she tells PEOPLE. “I thought that was an odd question.”

When Hutchins, her mother and Mila, were in their first class seats — with Mila fastened in her car seat — the agent “ran onto the plane” and rushed to the family, Hutchins says.

“He came over and told me that I can’t have [Mila] rear-facing and I needed to face her forward or else the plane couldn’t leave,” she says.

Federal Aviation Administration guidelines state that a child can be placed in a rear-facing position, but must be in an airline seat that is faced forward. However, airline staff told Hutchins that “strict” policy prohibited Mila from facing the seat.

“There were at least four people surrounding us and my daughter was screaming. They were very forceful, it was a really bad situation,” the new mom tells PEOPLE. “They were telling me I need to forward-face her or the plane couldn’t move. They kept telling me I was wrong, but I did all of my research and I knew what she should’ve been doing. They tried to make me feel like it didn’t matter.”

Hutchins did as she was told, placing the 18-pound child in a forward-facing position in the car seat. She says the plane immediately hit turbulence, and Mila’s head and body often jerked from the seat.

“I had to hold her head back, her body would go forward,” she recalls. “I was concerned that if we hit something bigger it could’ve been an issue.”

Shortly before the plane landed, airline staff approached Hutchins and apologized for the incident, admitting that they had been wrong about the policy. Hutchins was then able to position Mila properly for the landing.

She later spoke out about the incident in a Facebook post, writing that airline staff made her put her “child in a dangerous position.” She said they have since refunded Mila’s ticket.

In a statement to PEOPLE, an airline spokesperson acknowledged that the employees had been “mistaken.”

“At United, our customers’ safety is our top priority. We have been in touch with the customer and have apologized for her experience. We are continuing to review this with the SkyWest staff to learn more about what happened.”