Oh she'll weaponise the dog commitment.
She will wait until the day before / the day itself and ask what time to expect you. Then when you say you're not coming she'll reply.
I'm thinking something along the following lines...
"I am really shocked that after deciding to let down DD you've now also decided to let down an innocent dog too. I knew that you were for some reason angry about this even though you know I have to work and you have time to drive the girls. But I never thought you would take it out on an animal. We now have nobody to look after DDog so thanks for that. I'll explain to DD that not only can we not go to club any more, we can't go on a family weekend away either."
Or something like that. WON'T SOMEBODY THINK OF THE ANIMALS?!
Sorry she's been such a dick OP, especially as you said you hate confrontation.
This has been a really good exercise in sticking to boundaries though, you've done so well!
As an aside, your DD sounds really lovely and I think it's great that you've taken the approach to be the parent and decision maker but explain the thought process to her and take time to explain what might happen next and how to tackle it.
Enjoy your Friday car journeys together chatting away and having a nice time - she is your responsibility. It's not your fault that despite two years of generosity the mum won't sacrifice ten minutes a week to walk to yours.
Well done! 