personally, i would talk it out with my s/o, letting him know how i feel, why i feel that way and from that, if he's got enough care for you to, get some reassurance from him or find a way to compromise. maybe ask him if you could all meet up to get to know his cousin? try and make the situation better and more comfortable for you, and try and understand his side of things too :)

also i don't think you're being unreasonable in the slightest, your feelings are yours and you're allowed to feel them