I'm going against the grain here:

He told you this girl is family to him, and you straight away dismissed it and tried to control him by guilting him into speaking to her less, then when you met her you still kept dismissing her.

You don't get to decide if she's family to him or not. Your boyfriend is an oblivious, definitely, but you're staight up jealous and controlling. Your end goal was trying to get him to cut her out of his life before you even knew her.

No wonder she doesn't like you: You completely dismissed her before you even knew her because of her gender, and be honest it is because of her gender. We both know you wouldn't be too worried if this was his, as you call it, 'fake cousin'. You tried to come between them despite their long history.

From that moment onwards, any genuine complaint you had about her fell to the wayside, because you've already established you don't actually like her before you even knew her properly.

And to be completely honest, if I was in your boyfriends position, I would probably break up with you, before you decided that you're jealous of any other members of my family and I need to cut them out of my life.