3 are lovely easy children and 1 who whinges and whines all day about anything and everything.
I just know life would be so much happier for us all if we hadn't had her
It’s painful for me to read how you feel about your daughter; I can only imagine how painful it is for your daughter to sense this is the way you feel about her, as I’m sure she does.
You talk about your family as if you, your DH and your other 3 DC are your “real” family and this DD is just an interloper who has come along and messed everything up for the rest of you. It’s heartbreaking. She’s your child, just as much as the others are; yes she’s different, but why are you making that her fault?
She got her genes from you. She gets her environment from you. She’s SIX years old, FFS; the agency she has over her own life is next to nothing.
Yes, I can understand it’s difficult to have this one child who isn’t docile like the rest and who you feel is spoiling things for your other DC, but bloody hell. She’s your child too. As a pp said, behaviour is communication: she has needs that aren’t being met, and you need to start recognising that. You are her parents and it’s your job to meet those needs, to love her as unconditionally as you love your other “easy” DC.
Your whole post is about how she is failing as your child. Because it’s easier for you to frame it that way than think it’s you who are failing her as her parents, and recognise it’s on you to keep trying till you find what works for you and for her.
You can wish she were different and blame her for it all you like - the way you describe her it’s as if you think she’s a defective model that you were unlucky enough to be palmed off with - but that won’t achieve anything at all; will only make things worse in the long run.
She’s part of your family; she is your family, just as much as your three “lovely easy” children. She is not an interloper who is destroying your family, she is an integral part of YOUR family, and it’s your job to give her the parenting she needs, however you make that happen, whatever support you need to get.
And that starts by stopping blaming her and recognising that she’s not some outside alien force doing this deliberately to hurt everybody, she’s just a very small child who’s obviously not happy and whose distress it’s your responsibility to alleviate. Because you are her parents. And she is your child.