First, your son is your daughter's half-brother, not her step-brother. This may or may not matter to you or to her. But I think it's interesting that you use a more distancing term about their relationship.
I think the most important thing to bear in mind here is that your daughter is a teenager. Teenager's emotions are all over the place, particularly if their parents have relatively recently split up. It is particularly difficult for them to deal with one parent going off and starting a new family. For her it is as if you have not just abandoned but replaced her. You probably don't feel that way, but she may well.
In these circumstances I think it is absolutely wonderful that your daughter wants to see her brother. Seren may also be right to say that it is a way for her to see you without losing face, but, even if it isn't, it is something to be rejoiced about in its own right. It shows that your daughter wants to be some part of your new family and it has the potential to be a wonderful relationship for both of them. It doesn't matter that your daughter didn't show any interest when your son was ill. That was a long time ago in teenage time and in any case she may have been feeling much more raw and uncertain at that point.
Think about the positive aspects of this. If your daughter and son form a good relationship, then in the longer term he has someone nearer his own generation to whom he can turn to for help and advice. In a couple of years you will have the most caring babysitter your son could possibly have. When she sets up home on her own he will be able to go and stay with her, giving you and your partner time to yourselves.
Frankly, I don't know what the problem is for you here. I also don't see why your son's 'rights' could not equally well to be to get to know his half-sister. I have no idea what a court would say, but it seems to me to be a really bad option to let things get that far. Why don't you just let her see more of him, stipulating that you would have to be there too as she is too young to look after him on her own.
Sadie