Ok this too has touched a nerve with me as well, like others, and I have deliberated all morning thinking about whether to post.
I was a second child (not twin) abandoned by my mother (and my father went along with it) to live with my Gran. I was abandoned at 6 weeks and rejoined the 'family' around 1, so I don't have any recollection of it. From then on I was definitely second best.
Massive amounts of damage was done. My knowledge that I was not wanted haunts me. I've really struggled with the fact that if my own mother couldn't love me then no one really could, and at some point everyone will leave. A lot of therapy and love from DH and friends has got me to a place where it doesn't rule my life, or my child's.
But it's not JUST the damage to your daughter that I think you are failing to recognise. What about the damage to your beloved boys (if that is the way to access your heartstrings)? When they are men, maybe with families of their own, do you think they are going to understand your actions? Do you think they will understand their father's actions? Do you think they will respect you and think what you did to their sister was acceptable? My sister supposedly had a good bond with my mother but as soon as she was old enough to question why I, her sister, was treated differently it made her angry - very angry. And in many ways she has been as damaged by the situation as I was, despite being the 'wanted' child. Perhaps more so as she struggles with guilt over what she had, versus what I didn't.
Your boys won't forgive you for this unless you do everything in your power to love their sister, and at the very least welcome her back in to the home and ACT that she is equal to them. Of course you now don't feel the same for your girl as your boys, because you simply don't know her - it is your responsibility as her mother, whether you like it or not, to change this now. To put her first now. To nurture her now. And in the future, when she is an adult, be willing to look her in the eye and admit how you failed her but how you did EVERYTHING (and I mean everything) to get back on track.
Frequently I encounter things I find hard as a result of my childhood. Not least at the moment the severe grief I have over losing my grandmother, the one who loved me as a mother should have done. A grief none of the other grandchildren share or can relate to. Please do something about this now, and don't rob an innocent child of the love they deserve. And please, if nothing else makes you think - but if you love your boys as you say you do, just think, for one minute - if what has happened to your girl had one of them in her place. Would that not break your heart?