Good luck tonight Aimsmum.
This thread has pressed a few buttons for me, having been the victim of dsd telling her mum I smacked her and the boy next door to us. I hadn't and if you knew me and my views on smacking you'd know how ridiculous it was. Looking back, I think it was a reaction to dd's arrival.
I think you've handled this so well, you come across as so lovely and reasonable. I really wish dsd's mum had been like you've been as I would have been happy to meet with her and talk about it. And if at the root of it had been my behaviour in any way I would have acknowledged that and dealt with it. I didn't get the chance though, dsd's mum refused to speak to me or dh about it, other than to tell me she was "going to have me" and the next we knew she'd phoned social services (who didn't do anything). I could understand her believing her daughter, totally, and I felt awful because I was having to call dsd a liar (I didn't actually use those words, but by saying it wasn't true I was effectively saying that).
I'm not saying that this is the same as your situation, it quite clearly isn't. You sound so lovely, you seem to have sat back and really thought about this, and there's been no knee jerky, angry reaction. I think you've handled it brilliantly, you're dd is a very lucky little girl to have you as a mum. I'll be thinking about you tonight.