Your cousin's daughter sounds much like my daughter in her eating habits. If I always made meals of things that I know she likes and will eat, we would all be eating Tyson chicken nuggets, peanut butter sandwiches, cottage cheese, milk and juice constantly. I don't know about anyone else, but that's not a diet I want to have.
I did not begin foods with my daughter any differently with my son, but somehow, he eats a wide range of things and she eats almost nothing. My son has a few things he says he truly doesn't like...while I am not sure I truly believe him (I think he has just said he doesn't like them for so long that he's convinced himself that he doesn't when I really don't think he has a memory of ever eating it), I am generally okay with him not eating those things because they are few and far between and there are so many other things he'll eat. My daughter on the other hand declares that she doesn't like all kinds of things before she's ever even eaten a bite. And, then when told to taste things, she takes the most miniscule of teensy tiny, itty bitty nibble and says it makes her gag. I just don't "buy" it from her. I want her to eat better and a more varied diet. I do make her a separate dinner about twice a week -- generally it's a night when we all kind of eat what we want, but the other nights, she has to attempt to eat what we all eat. Now, if my main course is something that I know is a long-shot for her (like a salad or something very spicy), then I often substitute something in the meal. Like, baby carrots and natural style applesauce in place of the salad or maybe plain chicken wings if we're having spicy bbq wings.
If she doesn't eat her dinner, I generally do not allow her to get anything else that night. If she makes a good attempt but doesn't fill up, I will let her have some cereal (cheerios, kix or rice krispies)...but nothing more elaborate than that.
My kids stay with my sister in law one day a week this summer and my parents keep them about one night a month and I am a huge fan of them exerting their influence/power (ya know, sometimes it's other relatives that have the "power" with the kids to make them realize trying isn't so bad) with my daughter and having her try new things with them. I'd be very upset with her if she didn't attempt to comply with their wishes and deceived them by throwing food away (she's done this to me at home before), so I don't think what you did was wrong. But, it also sounds like her parents are unwilling to fight the food battle themselves with her right now, so your attempts aren't going to probably make her change on their own. Continue to make meals in which you know she will enjoy one part of it. If she eats the rest, great, if she doesn't, definitely encourage her to try, but don't sweat it if she doesn't.