You already have so many reasons for why you want this Bully Woman (BW) to back off. I would only use this one as an absolute last resort. It's also high drama and more likely to lead to a lot of gossip and exaggeration involving you.
I just think having read all the posts on here about reporting, that using this as the main reason will really backfire. Both the BWoman and her child are proven liars.. and it might occur to B Woman to use your excuse to say somethign untrue about the incident, in order to get her own back on you.
You don't owe her any explainations. Least said the better.. How about the following?
OP... Ive decided not to do any more play dates for a while.
BW .. But Why?
OP ... Because I just don't want to.
BW.. But why.
OP.. Because I am fed up playdates. I'm exhausting and I don't want to do it anymore.
BW. But I don't expect you too supervise playdates.
OP. Nevertheless.. I just don't want to for the time being and I don't think its unreasonable to have a break from playdates, so its not happening and that's all I want to say about it.
So sort of have different or repeated ways of saying no., Let her take offence.. its your best option. She knows exactly why you want to stop playdates So really it doesn't matter how you decline to continue. It will have the same effect, hopefully of stopping them. You may have to repeat it.
Then if friendship group says why.. all she can say is, OP only said she doesn't want to. rather than she's accusing my DD of lying about the fact that OP hit her.
I'm sorry I missed your post about BWs DH having an affair with your friend suspect that this is why she's been so hard to detach and also why she treats you so badly ( I base this on the way she responds to your complaints). There is no friendship there from her.
Would it work if your DH also said to her DH..something like
"Look your wife knows about your affair with x and she keeps coming round to grill OP about X. Something is bound to leak. So you need to stop coming round to the house and stop the playdates."
That should take care of the Dad.
As to the friendship group. If they all side with B woman.. then they are not friends either. I don't think they will dump you, but you could keep a low profile with them. I'd be very cautious about what you tell them about BW.. let them find out what she's like for themselves, unless there's someone you really trust.
I do think, its worth mentioning to the school, if they are at the same one... that you have had to ask the parent to stop playdates and mention some of the bullying behaviour towards your DD, and ask them to just keep an eye on things at present. Because then its on record.
I hope you get somewhere with this, it's a horrible situation to be in. Best of luckx