I still can't quite understand Hasebe - why does she refuse for her daughter to be "treated" by Ryuzaki?

I suspect it's a matter of principle for her. She seems very strong in her beliefs of what is right and what is wrong. In the beginning it was probably because she thought Ryuzaki was a criminal, a killer who showed no remorse for his victims. Then when she saw how people only wanted to use him and his powers and went completely mad in their desire to take advantage of Ryuzaki's healing, I think she decided not to join that crowd.

I also think that is why Ryuzaki finds her so interesting and appealing. She is the only one who is not interested in his powers above all else.