Employee trouble

I have a small team. We work in the healthcare industry but one that has a huge retail component. One staff member in particular is causing trouble amongst the rest of the team due to her attitude. It has caused a lot of disharmony and inefficiency. She also happens to be an extended family member of mine. I have had numerous one on one meetings with the team, along with several group discussions. I have outlined my expectations and the values of the business. However, behaviour and attitude is not improving and discord is high. I feel I am being taken advantage of. I am working with an HR company who are helping me work through the correct legal channels to find a solution. However I don’t believe things will change for the better with this staff member and I want her out of the business. I feel embarrassed that she is making a mockery of our family relationship and our employment relationship. I am waiting to hear back from my hr support company for advice, but I feel it will be looking like I am letting her get away with bad behaviour in the eyes of my other staff. I wish I could be honest with her and tell her it is not working out, and it would be best if she moves on but unfortunately if I do that I am open to an unjustified dismissal claim by her.