I really want to say something to those people who are saying shy people are dead-wood or not putting in the effort and making them work. I suffer from chronic social anxiety but am high functioning. Most people don't know.
i think I prattle. I try to engage in conversations but although I seem to be doing what you fantastically interesting people do, I seem to miss something out. I talk about the same stuff but it doesn't seem to work. I ask questions of others bit it's not the same.
When I am in a particularly bad place, I am hugely self-absorbed (yep your mum has me bang to rights). I go away at the end of the evening and deconstruct everything I've said, punishing myself for it. But at least some of the commenters here feel OK because they didn't have to do the extra work for me.
And then I move onto my appearance.
People have told me I'm calm and thoughtful, confident. But I know at best they are being nice. More likely, I tell myself, they're bs-ing me or mocking me. As I said, I'm self absorbed.
For what it's worth, I think the OPs cousin has guts to go to these family gatherings. As soon as she gets there, people who should know better, who should be more supportive, are pointing her out as 'the quiet one'. And she still turns up. I don't know if I would.
OP, I think you've been attacked for what others have said in support of you. I would say try not to be irritated; her behaviour is probably not deliberate. I would try to make a friend by being an ally. Maybe point out to those people who talk about her in a disparaging way (if they are doing this without being prompted) what they are doing and how it might be making her feel. They are setting her apart, which is unkind. Say hi to her ask her how she's doing and leave it at that. Continue to be nice but undemanding of her, and she might be more forthcoming.