I haven't read all the replies, but just picking up (no pun intended OP!) on something I've just seen about 'moving the child's hand', I don't think that would have worked either, as the parent would have no doubt started rattling on about their child being 'hit.' My own thought on what happened is that I probably wouldn't have lifted someone else's child, but under the circumstances, I don't blame you at all for doing so. Hindsight is a wonderful thing, and sure, if it ever happened.again you could call out and ask for the parent. Maybe though, if the parent concerned finds themselves in the same situation again, perhaps they will step in and take some responsibility for their child, instead of allowing them to spoil another child's turn. I think the parent's reaction here was probably because the moment you moved their child, they most likely felt embarrassed at the fact it was their child, and that they hadn't done anything about their child up till then. The focus then inevitably turns to them as the parent, and it is embarrassing for them to be the parent doing nothing about their unruly child. So they reacted by having a go at you, to turn that focus away from them. I've seen it happen so many times. I think it comes from just not knowing how to parent too, a lot of the time. I remember a good few years ago, a mother apologising to me after her son was told off by the group leader at the toddlers group, for kicking my little girl under the table deliberately. I hadn't seen it, because of where we were all stood, and the angle I was at, but the group leader had, and the mum from where she was stood could see exactly what was happening too, the group leader confirmed this too) but the mum chose to ignore the situation - that is, until the group leader told off her little boy, and only then did the mum take notice, but she was visibly miffed that someone had told him off, and actually blanked me afterwards when I tried to make conversation with her. I overheard her a few days later telling one of the other mothers how her son found it hard to mix with the other children, etc. At the end 9f the day, they were toddlers and they were learning. My little girl was struggling too, and learning as she was going along, but she wasn't kicking someone on purpose under the table, and if the situation had been reversed, I certainly would have removed her from the situation, told her to stop and explained why.
So yeah, maybe next time you would handle it a little bit differently, but in the wider picture, no one can really blame you for what happened, and let's hope it at least taught the mother of the child that she needs to step up in future, rather than ignoring what is happening and then getting upset when someone quite rightly isn't tolerating it.