How can I tell my friend that her son is a bully?

[Snowybird]

My twin sons (age 6) are in a class with a boy who bullies everyone in the class repeatedly. The kid is in trouble every single day and my son tells me he overheard the teacher saying to the bully, "you know you won't be allowed to come back here for year 3 unless you stop hurting the other children..."
The mother is a single mum, father absent, succession of live-in lovers, a baby by a different man who has also left. However she doesn't fit the stereotype which may be building up in your mind: she is a very smart physicist with a good professional job very near home and a full-time dedicated nanny.
All the other mothers shun her and just complain to the school.
I tried the opposite approach and told my boys to be kind to their friend, invited him over, tried to show friendship to his mum, offered repeatedly to help if her childcare broke down etc. She did respond and opened up to me a bit.
However my boys are now insisting that enough is enough, they won't play with him any more etc.
I don't actually believe that confronting her will have any effect because that's what everyone else has tried.
However the kind and loving approach seems to have run out too.
I am not a psychologist, so any ideas?

well my advice would be to speak to the school tbh.

How kind of you

What kind of things does he do to bully the others?

Do you think that maybe she (like her son) is a bit socially inept?

"Is X OK, only DSs say he's not been as friendly recently..." or something like that.

Contact the school about their anti bullying and behaviour policy and stick to what is your business and your concern, eg the well being of your own children.

I didn't mean that to sound horrible BTW but if she is that unapproachable I can't see anything you try making a difference.

If she is unapproachable, it may be because she has problems in a social situation?

Maybe her son has too?

Interesting responses, thanks.
Of course she knows that everyone is talking about her behind her back. She may well be "inept socially", and perhaps she is desperately trying to stop her child punching and hitting.
The school has presumably tackled her (must have done if we can believe the remark my son claims to have overheard) but the problem persists.
I am probably the only parent who has not complained to the school - maybe that's what they are waiting for to finally exclude. That's very unusual for a six year old, I believe and doesn't reflect well on the school either.

Oh dear.

He needs help. I wonder if the school are trying to refer him for help?

You don't need to confront her - just calmly tell her the truth. Get her over for a coffee and let her know why your boys don't want to play with her son. No accusatons or blame - just the truth.