Can I bring my younger sister on a child dependent visa as a British citizen?

In my family, me and my mother have British citizenship. My parents lived abroad (country A) ever since I was an infant and I was brought up by my other relatives in country B. After my sister was born she lived for few years in country A and then, she lived together with me for around 10 years. Therefore, we are very close to each other.

I came to the UK for my studies last year and want to settle here. It is only my father who doesn't want to come to the UK. And, since they are not separated, my mother and sister cannot come here on their own to live here. I am concerned that my sister might feel abandoned and depressed like I did as a teenager. Her studies have already deteriorated. My father has no objection of my sister being able to live in the UK, it is just that he does not want to move here. 

I want to know if it is possible to bring my younger sister on a child dependent visa on my own (based on relative) if I meet the financial requirements? Or, is it that unless my father also wants to settle here, my sister cannot settle here? Is it that visas based on relatives are only for those who need medical requirements?