I've been in a similar situation, where my mil was careless and my dd was injured, so i may be able to offer some insight.
After it happened, I was beside myself with worry about my dd. I was absolutely furious with my mil for being so stupid and my gut reaction was that she clearly didn't love my dd if she could thoughtlessly expose her to such risk, when I spend all day every day being careful and thinking everything through to the nth degree to keep dd safe.
With the benefit of time to calm down, I realised that of course mil loves dd; she's just not a sensible woman. I don't trust her to supervise dd alone and I won't again unless, over time, she demonstrates a markedly better attitude.
Dh, by contrast was upset for dd but just said "Well, it was an accident". It made me feel as though he refused to recognise that the accident was mil's fault . I felt that, since he didn't have this appreciation of just how bloody irresponsible mil had been, he clearly still trusted her to supervise dd. I therefore couldn't trust him to keep an eye on dd around her. So, in that situation, I couldn't feel that dd would be safe.
It took a long time and a lot of talking for us to fully understand one another in this. Once I knew that he recognised that mil could not be trusted to be alone with dd, I felt happy for him to supervise the pair of them.
Until your gf knows that you take her worries about your mother seriously, how can she trust you to keep an eye on her? That's your first step in fixing this. She's not punishing your mum; she's bloody terrified that her son will be injured again.