Exhausted Mom Carrying Infant finds Seat on Train, then Woman Beside her start Screaming

A young mom was traveling with her son in England. She found a priority seat in the first-class cabin and decided to sit there with her infant son.
The woman sitting one seat over was using the extra seat for her bag, so the mom asked her politely to move it so she could sit down. In the scene caught on tape by a fellow passenger, the mother said, “I asked you nicely to put your bag on the floor and I offered to put it up. I’m carrying a baby; you have to respect me.”
Scowling, the woman responded, “And you have to respect your elders and betters. People have actually paid to sit in this carriage.”
Apparently, the mother had paid for a normal ticket, but she entered the first-class cabin and found a seat reserved for elderly people, disabled people, pregnant women, etc.
Because she was traveling with a baby, the mother had believed that she was a priority passenger, so she felt that she should be allowed to sit in the first-class priority seat. The woman sitting next to her did not agree. The elderly woman tells the mother, “I don’t want a screaming baby.”
Frustrated, the mother responds, “He’s not screaming; he is behaving better than you.” As the two women argued with one another, other passengers joined in — some believing the mother was in the right, but more people yelling at her to leave her seat.
Eventually someone from further down the train in first class offered the mother a seat. She agreed, eager to leave the seat where she was being yelled at.
Do you think the mother was in the right in this situation?

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