Mum said 'don't be cross she was just so tired'
She knew you wouldn't want her to do this, because she said "don't be cross".
my mum called me mean mummy!
She did this when you enforced your boundaries. She did this in front of your child. That's manipulative on two accounts.
Then as we were leaving Mum started crying like I'd been really harsh?!
She could tell you were cross (rightly so) and this was a Manipulation Of Last Resort. Don't fall for it.
And I usually bite my tongue when she goes against my wishes but this just really grated on me.
You bite your tongue because you know she'll kick off when you don't. And that means she gets away with all sorts.
Stop biting your tongue around her. Start speaking up. You don't need to be rude, but you do need to start making your boundaries and your feelings clear. Tell her, briefly, what she's done that is unreasonable, and how you expect things to happen in future. Don't get drawn into discussions of why she did these things, or of how unreasonable you're being: just be clear, set the limits, and move on.
If she can't cope with that, then walk away for a while. She will either learn to be better, or she will ramp up her bad behaviours.