Sorry, but I'm with your girlfriend on this, I wouldn't let either my mum or my MIL be in sole charge of either of the DCs if they'd suffered injuries like this in their care. It does sound neglectful - did you girlfriend have concerns about your mother's attitude to risk before? I can't understand why anyone would be so blind to the danger that a cable from a kettle would be in reach of a toddler and ignoring what hte toddler was doing so that they got at it. He was in her arms while she was close to a boiling kettle, why? Why didn't she grab his hand away? She might be asking herself these questions, but it could easily be that she just didn't see the risk. And she should have done.
that your GF is insisting on being there too could be just her fears (she let her perfect DS out of her sight, and he was damaged so badly, she's uncomfortable with being out of his sight), or it could be that she doesn't believe when with your mum you will be in charge.
OP, do you tend to defer to your parents when round them? Did you see the risk of what your mum was doing? If you genuinely think it was freak accident that couldn't have been avoided that sorry, your attitude to protecting your DS from harm is no better than your mothers.
Until you and your mother accept that was an accident that was avoidable, you aren't going to make your GF think your mother is safe to be left alone with DS, and your GF doesn't trust that you are concious enough of the risks to not leave your Mother alone with DS.
Plus the simple fact is, cutting your GF out of your mum's life isn't going to heal the rift between them. It might be that actually, it's good that your mum and GF are forced together, so that she can get to see your mum isn't some terrible person and little by little the tension should ease. (However, accept she may never forgive your mother. This is reasonable, so long as she's polite, your mum fucked up massively, few parents could forgive that).