Ok. So we talked the whole way there, and a bit more when we got there.
First I brought up the initial situation and gave my side of it.
She insisted I wasn't in the wrong, that I had done the right thing, behaved in the right way, that my sister had overreacted, has form for doing so, and that she needs to resolve her own issues. All lovely to hear.
So I asked why she didn't say that to my sister. Why she agreed that I was volatile and unreasonable etc. She denied it. So I showed her the messages. She went very quiet, started crying, and said its easier to agree with my sister than go against her, that she couldn't face my sisters anger being directed at her, that she didn't mean it, and that that was before she had heard my perspective. That my sister had told her a whole heap of (lies as it turns out) stuff I'd said and done. She said its a balancing act to keep both of us happy 
She says she is very sorry. Will never talk about me and my family to my sister, etc.
I'm not going to trust her again, and I'm certainly going to take a step back, but I am going to forgive her. I know my mum and she never means wrong or harm. And I love and like her. I'm just pissed off at this. And she won't forget it, she saw how hurt I was. I explained that she should have listened to my side before agreeing with my sisters.
I've found it very difficult as I've worked hard to overcome major anxiety, which in the past has left me labelled as controlling or volatile by my family. To know they were still doing it despite all my efforts really hurt, and I think seeing that has upset my mum. She knows she has fucked up.
She really isn't a game player. This will sound harsh but she isn't smart enough. She is quite easily confused and makes mistakes. A big one this time.
More importantly, she seems now to support my taking a step back from my sister until she addresses her own issues.
Can't believe this became such a big thing! I'm glad I spoke to mum about it and cleared the air, as I was stewing. And I'm glad I know that she can't be trusted and that she knows my sister can't be trusted. Pretty sure my brother is her favourite btw 
One day, when this is over, and the situation occurs, I will say how upsetting I find it that I have to face my sisters grief over my daughter. It's unfair.