you have to show you have 'sole responsiblity' for your child, you say you have 'full custody' of her, but then shes brought up by her father, and if you leave her to come to the uk, you will be leaving her with her father. iam no expert but if they interview her at the embassy, you might have problems with showing you have sole responsibilty.. the embassy might not like that her father is a major influence on her, last thing the embassy will want is to take a child away from a parent.
i've got my stepson here when he was 17, he had to go for an interview, they asked him about his father, but his bio father name was not on his birth cert, also his bio father lives in america, and we got him to write a letter of 'no support' meaning he never really had any contact with him, didnt support him financially.. and that he wanted his son to join his mom, sister and step dad in the uk.
also on your spouse visa, mention that you intend to bring your daugther to the uk when you are settled and when she has finished school.
but dont leave it too long, if she turns 18 without ILR, she might have a major problem getting ILR if she is 18+
good luck thou.
