Expected - as occasional incidents - yes, acceptable and tolerable as ongoing behaviour, no.
Ultimately I would expect the (other) organisers to act. I don't buy the 'there's nothing we can do' line at all. Playgroups are generally privately run, by community organisations, they are not a public right. The organisers can have a quiet word with the parent, offer to help step in with the child. Ultimately they can say the child / parent's behaviour is not compatible with the group and they're not welcome back (though I'd hope they'd try to identify some help for the mother, or point her to someone who could).
The mother may well feel helpless and resigned to something she hasn't been able to tackle successfully, so may welcome help or even others' direct intervention.
Dd is a toddler and learning to negotiate toddler / child / baby interaction is an ongoing learning expeirence!
She used to 'hit' open-handed as a greeting but with suitable encouragement / discouragement she's modified it to stroking hair / faces, moving on to arms. Still not welcomed by many children!
She is very keen to interact with others and I spend a lot of time telling her that 'I don't think that boy / girl needs your help' (some older ones, 4+ are very gracious and let her 'join in', 2-3yos generally agree with me, sometimes the same-age ones find common ground) and have said to other children 'I don't think she wants that toy in her face' etc. I am careful not to 'tell off other people's children' so don't say 'don't do that' but with obvious, repeated hitting, I'd go for a stern 'we don't hit'.