I wonder if there isn't a bit more to it, actually. I'm not diagnosed but have many autistic traits, and what I have realised about how I behave in social situations is that it is, to an extent, performative. I can function quite well socially, but I am speaking, using facial expressions and using body language that I believe from years of observation to be appropriate to the situation. In a sense, I'm putting on a different "me". And it works - people respond well and seem to like me.
That may sound ridiculous, I don't know. But it's what I do. I've done it since I was at school.
It is hard, sometimes impossible, to do this around members of my family. I feel as though they know how I really am, and therefore can see what I'm doing and how false it is. Their observation freezes me up so that I cannot be the "me" that I need to be in social situations.
For example, I would not want to join a book group that my mother is in, even though I get on well with my mum and I would love to join a book group.
And at 14 I would have hated for a sibling to have come into a group where I felt a had a place and was comfortable.
So I may be projecting, and I can absolutely see that, in a "normal" family dynamic, the DS in this situation might have a perfect right to join the group, but I do sympathise with the DD.