Chloe, you need to write everything that happened down and then speak to the supervisor involved first. Tell her that you were not happy about the way she handled this situation and ask her to apologise to the Mum. I know what bullying feels like - I was bullied by the supervisor of my last job - it is not nice. If supervisor refuses to apologise and change her attitude then report her to your EY Development Officer. This needs to be stopped now before it escalates
Big hugs to the Mum.