I also think this thread has got way out of hand, but that is the nature of Mumsnet at times. Posts are painstakingly dissected and over analysed just so that some posters can be judgemental and form their own conclusions.
I stopped reading after I posted the first time.
But vr6lee you sound very level headed and I congratulate you for taking the initiative to resolve this very tricky situation.
Can I suggest that you sit your gf down and talk to her. Listen to what her fears are. Has she had concerns about your mother previously? Does she feel your mother interferes? Is she afraid of this happening again? Would she feel differently if it had been someone else who had been responsible, like her own mother or you?
Once you have listened to your gf you will have a better understanding of her pov and at this stage it really doesn't matter if you agree with her or not, don't offer an opinion, just listen.
She needs to know that you are taking her points seriously and are not dismissing them.
Give it a couple of days afterwards and have another chat with her. Raise the points she made and see if you can reach a compromise. Be prepared to accept most things on her terms and perhaps give it a deadline - agree to support her completely on her terms for 3 months say, then set a date for another discussion to see if you can move forward.
You also need to talk to your mum with your gf's approval. Put some of your gf's points to her and gauge her response. Tell her that you understand what a shock it was and that it was a complete accident, but she simply MUST understand her daughter-in-law's point of view and be willing to compromise.
Either she takes it slowly with your gf or she runs the risk of ruining the relationship completely.
Your gf may well blame herself for this, for not following her instincts perhaps in letting your mother care for your son. If your mum was doing her a favour (was she working?) then she might feel even worse, perhaps thinking it was her fault for not being there, for needing childcare, etc. Mothers find any way to blame themselves, we can't help it.
She needs your support and your understanding.
My little boy broke his two adult front teeth last year and bit clean through his lip whilst at school. They didn't send him home. We spent that night with him in A&E as he vomited and shook in shock. I still go over the incident time and time again. It was only minor compared with what happened to your son but nevertheless it affected me badly and so I can only imagine how your gf feels.
Now do take her out for a meal. She needs a break and she needs to be reassured. Remember that her and your son are your family now and their needs trump those of your mother. Harsh, but I realise that one day I will be second in the life of my son too.
It's bloody tough being a mum. Your gf needs some TLC.
And very well done in coming back onto this thread, that must have been hard considering the criticism that's been levelled at you.