INFO—dunno what the GF's r/ships have been like in the past. Has she had many other BFs b4 u who's just upped and left? Has the mother been supportive of her when she divorced the kid's dad? If the mum had been supportive of your GF then chances are she was protective of her daughter and grandson. She did not handle this well though. No, I don't think you should've ignored her. I think u could've responded differently though. Like don't answer her accusation but answer the reason behind the accusation. For eg, when she said u're just a temporary fix and that u'll leave them eventually, I'd probably have asked her why she thought that. U don't know what happened, did the same thing happen to her, personally? So is this projection onto her daughter and you? Rather than saying to the kid that his grandma is a liar, deal with her assumptions. Just expose it for what it is, her insecurities and fear for her daughter or her wrong assumption.

If it wasn't something from her own personal history and if she hadn't been a supportive mother and this is just an attack then by addressing the accusations u'd also expose it for what it is—just a personal attack. Like when she says it's cruel for them to just pretend like u'd stay, "why do you think I won't stay? You don't know what I'd do. You don't know what would happen. You don't know me and you haven't even tried to know me."

Plus is she also scared that u'd steal her daughter and grandson away from her? Does she have her own social circle or is it just them? It's hard to know how to tackle this until you know exactly what prompt her to behave the way she did and say the things she did.

I don't think this is a big deal, tbh. U sound like u love your GF and her kid so u're in it for the long haul so I'm sure u'll endeavour to do the best to stay with them, incl making sure the grandma feels secure abt leaving her daughter and grandson with u. I'm sure u can make this work and patch things up with her. I'd prob start with apologising to her for calling her a snake tho. Maybe have a coffee with her and try to get to know her concerns. Don't expect that the coffee chat will be congenial tho. I mean maybe she's been the fort for her daughter for many years and she's just very protective of her, as is expected. Just expect that it might be a challenge trying to understand her, that's all.

Good luck.