If the DD did pinch her and it was about to go further, I can understand the smack. There aren't easy answers to children (even as Adults) who attack their Mothers (in the case of other Girls/Women).
My DD has ADHD. I was battered by her until she was around 19, then I'd had enough. She seemed to control herself around other people, she had got into the habit of doing it to me.
You can say violence doesn't solve things, but my retaliation would stop her in her tracks. It meant I wasn't in for a pasting.
It was only after another Police incident, a couple of years earlier that I started to see it as a form of DV. This is discussed at length on all SN Boards.
The Mother might be abusive, or she might not know what the hell to do when her child physically assaults her.
In ordinary circumstances, or in the case of under 18's, no, you shouldn't hit back, I agree with that. Even after that, it should be just defensive.