partner's child

I presume this is a verbal embargo? It depends how sensitively your son can manage to impart this news to his partner. If he can bring it into the open in a supportive and non-judgemental way, it could pave the way for change. I'm wondering why this young child is so 'needy, jealous and troubled' ...

Could you not offer to babysit and have a special day together?

I think your son should be up-front and honest with the mother. They need to discuss the child's behaviour, and the mum needs to know how bad the behaviour is in other people's eyes. Why should it damage the relationship? The mother should be glad your son is taking an interest in the child.

It's obviously quite normal for the child to be jealous because she will have beenquite happy with her mother and won't necessarily have wanted anyone else in the relationship. But it is a problem if her behaviour has become disruptive enough to affect other people. Can he approach the subject of the invitation by asking his partner what she thinks about the embargo and what she feels should be done? If the subject isn't raised it looks as if they will face a future not going anywhere. How do her friends feel about the child? Is there someone among her friends or family who could have a word with her.?

Is the little girl at nursery or in Reception class? If so what is her behaviour like there?
If it is OK elsewhere then clearly it is a relationship issue and not a behavioural difficulty, i.e child can control behaviour but chooses, in some situations not to.

This is always tricky for an 'outsider' to point out. Perhaps she is afraid she will lose her mum's affection, feels insecure and does things to get attention.. because for unhappy kids any attention is better than no attention. I'd be trying to ignore the tantrums and setting up a star chart or similar given each time she complies with a request without a fuss. 10 ( or whatever number)earns a special time with mum: a swim, a trip to the park etc so she see compliance will get her attention she wants. Each star/sticker also earns a big hug and a verbal reminder of the goal, e.g well done you did what I asked straight away. (Hug, hug) only four more stickers an we will be off for fun in the park on Saturday'

Re the invitation.... think the issue needs to be faced. tough to do I know but honesty always best in these situations especially if DS can be really supportive. Mum might be relieved to have time away from her demanding daughter!