Someone sitting by while their kid bullies others? Sounds a bit slack to me.
Actually, based on some info above I think it might be an over enthusiastic application of a parenting philosophy like radical unschooling or Taking Children Seriously rather than simply slacking. It could be worth the OP doing a little further digging with her source to see if the original info came with certain key phrases like RU, TCS or "non coercive". If it did then that would point very strongly to a philosophy based strategy being in place. And becuase the philosophies themselves are quite extreme when compared to the more mainstream variety they can be quite fixed positions. If fixed, resolution or mutal understanding can be harder to come by with the more typical indirect "oh shall I parent your child for you? watch me do it" or direct "would you mind terribly stopping your child from walloping mine ?" because those can be viewed as actual persecution from wrong headed sheeple, while the natural irritation of parents watching their kids being regularly clonked gets minimised away to irrelevancy.
I personally wouldn't want to be stepping in and correcting the child directly when the mother does not under those circumstance ever again, because that can increase tensions dramatically and then it gets so much harder to resolve with any tactic other than voting with your feet because parental backs being massively up on both sides just polarises postions further.
Maybe wording an approach to mum along the lines of "I understand you don't want to coerce you child, but I'm sure you understand I don't want my child coming to see other kids as something he needs to be fearful of, can we talk about finding a way so both of us and both of our children can spend time here in a positive way ?"
(I know it's wordy but certain turns of phrases might reflect back the "fundamentals of philosophy" so they might get heard)
I think even somebody who has spent so long on certain parenting forums that they have absorbed a persecution complex by osmosis would find it a struggle to treat an approach like that as purely hostile to them and their value system.
I wouldn't put money on a solution actually being found, because to put it bluntly, the philosophy can be pretty cemented in place, particularly with younger children, but as a way to crack open the door to see if she will make concessions within her parenting philosophy in order to rub along bettet in a social settings I think it is worth a try.
If the OP gets feedback from her along the lines of "other kids are just going to have to suck up being collateral damage" in the name of her parental philosophy so her child doesn't become irrevocably damaged by the occasional redirection or the odd outright "No, stop it", then I think there are only two choices in terms of speedy resolution.
One is to take it up with the organiser and ask what their policy is when users of the facility never intervene when their child is persistently hurting other children and see if that gives the heads up that tensions are brewing and it's time to be a bit more proactive at communicating what is required of parents in their faciltiy before people start voting with their feet and warning others to give it a wdie berth.
The other is to vote with feet, or accept that being at playgroup means off chair, on carpet full time ready to provide a large human shield the whole time your toddler is there.
Not perfect solutions, but then easy perfect solutions are infrequently on the table when parental ideals and values clash in a social setting. And that reality doesn't melt away thanks to uninvolved outsiders bandying around "just" like it was a magic wand.
In the OP's postion I would grab a few phone numbers of the mums I liked best and go for meeting up indpendantly instrad. If playgroup is more stressful than it is nice for parent or kid, it's worth knocking on the head in favour of other socialble activities. It's a pity when the one local to you has issues that make it less than appealling, but unless the organisers are prepared to have ground rules for parents and remind people to respect them, there isn't really all that much you can do about it.