If you read the whole thread Mikulkin you will see that there has been a long established pattern of bullying behaviour from the older child towards the youngest. This is not one single incident.
In addition, the older child is never disciplined - no matter what he does - so feels able, and inappropriately, given both his age and the fact that he is not the most important member of the family, to effectively lay down the law and "refuse" to come to the OP's house unless she "apologises".
The boy's father has made no attempt to explain to him that this is unreasonable. In fact he's done quite the opposite for around a year now - rewarding a long history of spiteful behaviour with expensive presents and flash days out. By doing this he's sending the message to his son that he (the dad) thinks his wife was in the wrong for having the temerity to tell him off when he was particularly nasty (and it sounded long overdue). So the dad has undermined his partner, and basically given him no reason to come back to the house and have a normal relationship because, most 15 year olds would find it far more attractive to keep playing the drama queen when they're rewarded so strongly.
The OP has not banned this child from her house BTW. She simply and quite understandably doesn't want to place her DD in a situation without her where again and again she's been subjected to nastiness by a much older and bigger child. Past experience has shown that very sadly, she can't trust her DH - DD's own father - to deal with any such behaviour from the older child in an effective manner .... where the bully would be disciplined, and where the younger child would therefore actually feel like her own dad gave a flying fuck about her wellbeing.
Of course, I concede that maybe the SS won't be sly and nasty again ..... but good grief, in the OP's shoes would you really take that risk in the light of such a significant back history ? Why the hell should she expose her daughter to that risk, knowing that her DH will almost certainly turn a blind eye, make light, and quite probably hide any such incident from the OP ?
"If he is not nice to her she will tell and you can stop contact again" ...... riiiiggghhhtt, so it doesn't matter if SS thumps her because hey, she can stop contact again and all will be right with the world. FFS - how will that little girl feel if her brother hurts her and her own mum hasn't protected her by sending her into that situation. Plus of course her dad won't give a damn because he's too scared to rock the boat with the boy-who-can-do-no-wrong-no-matter-what-he does.
Let's not forget what a nasty shit the dad here seems to be too. He's quite happy to mess with his own daughter's mind - deliberately upsetting her and goading her by repeatedly telling her what a fantastic time he's had with SS. Apparently he does this so the DD "knows" how unfair her mum's being. In other words, he's using his daughter as a weapon to get at his wife. Regardless of the psychological damage he could be causing. He's pathetic and irresponsible.
And I should imagine that if DD was being bullied at school, for years, where no-one was taking it seriously, and the bully was never disciplined, and the school appeared not to care, that the OP probably would keep her away from such a school ..... just as many poor parents have had to do when their concerns weren't being addressed properly (this topic crops up on these boards quite regularly).
I personally think the OP should LTB, and insist that future contact between dad and DD takes place under supervision because he simply cannot be trusted to look after both his children with equal care and concern. In effect, it reads to me that he's prepared to sacrifice the well being and safety of his younger child in order to keep the older one "sweet".