Hi Mrs-Astley, if I was you, and her Dad agrees, then I would let her do it. At that time of life a lot of girls can get seriously confused (I for one) but I don't imagine it would last long. Maybe she could just stay with her Dad for a couple weeks, I bet she would soon miss home and want to be back with you. If you haven't (or she won't) sit down and talked to her about it then let her see for herself what she wants to do. If she wants to stay then it may be sad for you, but you know she will be looked after well, and you can somewhat concentrate on your other kids. I know it's hard, but she probably wants to be with her older sister, at least for a while!
Hope this helps.
All the best
;) x