I am just so happy I never took my sons to parent and toddler playgroups! going on this thread, half the parents would have hated us!
I had a feeling at the time that playgroups were more trouble than they were worth. I felt - still feel actually - that any regular meetings of parents and littlies are doomed to failure unless a professional non parent person (s) has oveall responsibility for all the children. My sons did their socialising at nursery and childminders. I realise this is less of an option for SAHMs. TBH going to parent run playgroups is one reason I'd find it hard to be an SAHM of babies and toddlers.
My two sons were lively, sociable toddlers. Both went through biting phases (a very brief one in my ds2's case). MY ds 2 was better at playing nicely with other toddlers. My ds2 was prone to get too overexcited and hit out. Agree with hmb, you get what you are given. I strongly dispute that all biters or hitters are the product of uncaring parents who do not watch and discipline.
I'd have no qualms about telling off another child, but only in a matter of fact way as in 'it's wrong to bite, stop it' rather than 'you are a nasty child for biting'. If the child's parents overheard you saying the latter they could IMO be justifiably be cross with you. Two wrongs don't make a right.
If you feel uncomfortable telling off in public do distraction instead. Get the biting child interested in someting else - get them to move away. Or do both - ' it's naughty to bite, don't do that followed by look, they're getting out the toy cars over there....'
Little tree, going back to your situation, I wonder if a nearly one year old is old enough for that particular playclub? don't know much about these things, but could you find one for under 2's? three year olds don't mix that well with babies IME. Rough play is a fact of life for older toddlers but as you've seen this isn't always good for babies. 3 year olds aren't technically old enough to be thought out bullies as far as I am concerned, though they can do bullying things. FWIW I think you were right to intervene as you did. But I think this play club isn't for you.