AIBU to tell off someone else's child

No, in those circumstances, I don't think you were. If you'd gone over to the carer to point out his behaviour, he could, in the meantime, have done serious harm to your GD and no doubt you would have received a mouthful of abuse from her anyway, by the sound of things.

Yes, you were. You could have spoken to him quietly at an earlier stage, when he was just pushing her out of the way, before his behaviour escalated into kicking, and if that didn't work, you could have removed your GD and spoken to the boy's carer at that point.
Personally I wouldn't have bothered. I would just have taken my GD to play on something else and if the boy came over, just said my GD was playing on the whatever it was and he would have to wait.

Telling off someone else's child, whom you have no authority over, when the adult is present isn't acceptable IMHO.

Yes there was no way I would have left her to do that. It was about 20 minutes she was on the phone without going near the boy. He was only about 5 so not like he didn't need an eye keeping on him anyway. He was big though and strong. She was very upset after the kicking

But jane this is exactly what I did do. I did speak to him quietly and nicely and he ignored me. We moved away to play on different things several times and he followed. I don't see what else I could have done. I used exactly the techniques you suggest so don't really see why I was unreasonable. The other adult was not really present in that she was on the other side of the playground and completely ignoring him

Jane - I tried to be polite and say things like she won't be long and then it will be your turn etc but this did not work.

Having been a social worker and a teacher I think I know pretty well when a line has been crossed when interacting with other people's children - and in my view you did not act unreasonably. In a similar situation I once called out to a parent to come and supervise her child whose behaviour towards other children in a play park had become increasingly unacceptable and downright frightening to some. The mum was very angry at being 'called out' so publicly, but I calmly pointed out that I had seen her deliberately ignoring the offending behaviour. I think sometimes we intervene too little when bad behaviour happens in public spaces.

But it was obvious to you that she was his carer workernan, so I still think it would have been best to approach her before telling him off, as opposed to speaking quietly.

By telling him off all you got was a defensive reaction and the boy will have learned that if he bullies younger children and someone tells him off, his mum will come and stick up for him.

If you'd approached the mother first and drawn her attention to his behaviour, yes you might well have got a mouthful of abuse, but on the other hand, she just might have got up and told him off herself.

But jane, workernan did try speaking calmly and quietly to the other child and he ignored her, she did move to other things and he followed. The other carer was not, it would seem, taking good care of her charge, being too far away and engrossed in a mobile phone. It's easy to make judgement when you are not present, but I think workernan explained the situation clearly.

Absolutely! if the child's mother/carer/nanny couldn't keep an eye on him, when he started kicking her your reaction was justifiable given there was no one giving him guidance on how to behave.

No, I would of told him to leave her alone too.
And when the adult who was supposed to be supervising the boy acted like she did I would of told her a few home truths too. If she was the type to give you abuse, without calmly wanting to find out what had happened, she probably wouldn't bother stopping him in the first place.

You see far too many people glued to their phone screens and ignoring children these days, they haven't got a clue what they are doing or sometimes even where they are. I've seen parents carry on walking along at school times, head down and tapping away while the child stops. They could be in the road, off in a different direction, hiding or anywhere and the adult no idea.

You did absolutely the right thing in telling this child to stop hurting your grandchild; he has already learned that if he bullies younger children his carer will not intervene. Her instant response to you shows that she was well aware of the child's behaviour but had no intention of taking any preventative action herself.

Hmm..a tricky situation. There is always an assumption to the worst scenario: uncaring parent/ bullying child etc. May not be the case.
Your job was to keep your DGC safe. I might have removed the child I was caring for and then spoken to the child's carer explaining what had happened.
As you didn't know if it was mum/nanny etc. or if child had a particular need or have been a sad and poorly parented child communicating directly with the responsible adult is a better option than with an apparently misguided child you do not know.

Had the child's parent/guardian been paying attention, instead of staring at her phone, she'd have been aware of the situation and could have dealt with it before workernan had to. OP tried to diffuse the situation, calmly and politely, but the child ignored her. IMO, the reaction from the parent/guardian was borne out of embarrassment because she knew she should have been paying attention and dealt with the child's behaviour herself. I'd have done the same as workernan or worse.

The child was only five so I think speaking to the person he was with would have been my choice.

which is what I would have done, or I would have continued to do what I was doing by moving away or saying nicely it would be his turn in a minute.

However when someone of any age is kicking another child viciously and aiming for their head what else can you do apart from remove the child in your care (I did but it was hard because of where they were and I got a kick in the process) and try to stop the other child from doing it. The other woman was not looking, not interested and not close enough to pull him off as quickly as it needed to be done. I didn't use any physical restraint as tempting though it was. I just told him to stop kicking and that it was not a nice thing to do and he would hurt someone , he had already hurt someone.

As a child I lived on a large council housing estate where we played outside and where we were often socialised into the niceties of life by neighbours and indeed by passing strangers. We expected that adults would intervene if they spotted that children were behaving badly and the phrase, 'just wait 'til I see your mum' was often heard. We saw such intervention (interfering I think we would have called it then) as social lessons in which we learned that there are limits to how far people, other than parents, will tolerate poor behaviour in public.

No question I would have said something to the child who was misbehaving as well as moving my own child.
It seems a screen was taking priority over child care in this instance.

I would have spoken to the child and told him to stop right there! Then to the parent/"carer" and explained what had happened. If that person decides to sound off at you, then so be it. You can't stand by and watch your GC being abused.

exactly

Something like this happened to my DGD once. We were in a rather long and tedious queue for to see Father Christmas, in a barn setting, with regular colouring tables enroute. She was only just two, and a rather larger boy of about 6gave her a really hard shove that made her fall over when she tried to join in on one of the tables. I rushed over, picked her up and told her very clearly that some people were just nasty. All the while glaring at this child and wondering where his parents were. The queue was almost static, so we sat down on a hay bale and I spent the next 20 minutes glaring at him. At one point I did the 'I see you gesture'. Think I scared him to death, but TBH - I didn't care. My DGS's would have been hauled over the coals if they had done the same thing to a much younger and smaller child. Tiger Nanny was not having it! I am usually much calmer, but his rather nasty attitude rattled me.

Sorry - by the way - I think you were right!

What a cheek of the person who was supposed to be looking after the child to have a go at her. I'd have said in a matter-of-fact way something along the lines of "If you hadn't been glued to your phone, you'd have seen what was going on and not be having a go at me now".

Honestly, the "phone brigade" need to catch a wake-up.

I mean a go at you, workernan.

workernan ignore the critics, you did absolutely the right thing.