Back away slowly and run... don’t look back.

Her cousin is definitely gay but won’t admit it

I hate to say this, but maybe it's best not to persue the relationship any longer. Your girlfriend clearly has a toxic relative who is trying to sabatoge the relationship. This won't be the last time he pulls something like this, and it'll only get worse. She was also quick to believe her asshole, toxic cousin over you without evidence. Would you really want to stay with someone who not only has a horrible relative willing to kill the relationship but who is easily fooled? Whichever decision you choose, I wish you luck.

I hope he is not saying this to instigate a threesome.

Seriously though, sounds like this family has more issues than vogue. Run.

Clearly the cousin is a female. Multiple people have made the same wrong assumption. Says something about our society...whether that is about reading comprehension or sexism regarding homophobia is up in the air.

Get rid of her if she believes her cousin over you! She is not worth the agony!

Someone needs a punch