It is not at all unusual for your daughter to make this statement. She is jealous of her cousin. My granddaughter has frequently said she wants her brother to move out. So perhaps it is unusual for your daughter to want to move out instead of her cousin to leave.
Perhaps your daughter senses that her mother prefers the cousin. You say your daughter gets "spoken to alot." Is the cousin quieter, perhaps more easy going and easier to get along with? If so I can understand why your daughter might think her mother prefers the cousin.
To remedy this it might help if her mother and you frequently tell her that you're so glad that she's your little girl. Catch her doing something right, no matter how insignificant it may seen, as often as you can, and make a positive comment about it.
It sometimes seems normal to compare children. I often heard the words, why can't you be as quiet, good, funny, smart as your sister sort of comments. Or, your sister doesn't do that. Or, Do what your sister does.
It would be easy to say in anger, why are you so rambunctious? Or why can't you sit still? I hear that often at my daughter's house.
What helps is to tell the child specifically what you want them to do and what the consequence will be if she doesn't do it. At my daughter's house it sounds like this. "You spilled your milk. Please go get the dish rag and clean it up." or for my grandson "I want you to sit on that chair and eat 2 more bites before you get down to play." He knows that if he doesn't do that he will get sent to his room until he can come out and say, sorry, and eat those two bites or until dinner is over for the rest of us. It's not so much a punishment as a way to teach him to obey and to give the rest of us peace while we finish our dinner.
It's important to handle situations before we become so irritated and angry that we discipline in anger. Decide what the rules are ahead of time. Tell both girls what you expect, and discipline them in similar ways. This is just an example. The younger child fidgets at the dinner table and she's excused even tho she hasn't finished her dinner. The older girl, because she is older, is expected to not fidget and is lectured about not fidgeting.
We do have to take into consideration differences in expectations and discipline techniques depending on the child's age and temperament. At the same time we also have to keep a balance so that each child knows that they are loved.
Since the cousin doesn't live there it would be easy to treat her differently than your child. It would be easy to treat the 4 yo more like a guest. At 6, your daughter wouldn't understand that even if you tried to explain it to her. She won't understand that because she is older she is expected to behave differently in some situations.
The way to handle that is to be sure that you praise her more often than you discipline her. Focus on interacting with her as well as with the cousin. Build up your daughter's confidence in your love and her ability to be lovable. Do some things with and for your daughter that you don't do with the cousin. Let her know she is special because she is your daughter. That you do love her cousin but you love her best.
If you or your wife haven't spent much time with her, focus on sitting down with her and playing whatever she likes to play. Build with blocks, play Barbie, watch a video. When you do watch TV with her pull her close to sit next to you even if she moves away. She'll grow to expect and like to sit next to you. If both girls are there, pull your daughter into your lap and have the cousin sit next to you. It is right to show your daughter a preference while you continue to pay attention to the cousin. Taking turns is a way you could handle this. Daughter sits on your lap for 15 minutes and cousin for next 15 minutes.
Does your wife insist that your daughter play with and be nice to her cousin all of the time? If so, it's normal for your daughter to want to not always play with her and to sometimes be angry and need help learning how to handle those feelings. Telling her to "be nice" is often the only instruction a child receives. Children have to learn what "to be nice" means.
I also suggest that the cousins clothes be kept some place neutral and definitely not in your daughter's drawer. That probably feels too much like an invasion. Put her clothes on a shelf about the hangers or in the hall closet.
I may be way off base with these suggestions because I don't know what actually happens at your house. These are ideas for you to consider.
This may be similar to sibling rivalry complicated by the fact that cousin doesn't actually live there. Adele Faber and Elaine Mazlish have written a book which is also on CD about sibling rivalry. It is easy to read and has actual examples that work.
