The way I read this is that your Mum parked in a disabled space leaving the badge on show and with the disabled person staying in the vehicle, who then removed the badge from display.
According to blue badge rules, this is not permitted and the disabled person must leave the vehicle, therefore, any fine or charge is justified.
https://www.gov.uk/government/publications/the-blue-badge-scheme-rights-and-responsibilities-in-england/the-blue-badge-scheme-rights-and-responsibilities-in-england
Note this para:-
You should not use the badge to allow non-disabled people to take advantage of the benefits while you sit in the car.