Is it appropriate for a PI to appoint someone who is a family member?
The rules differ from country to country, university to university, and department to department. 

On a practical note, I would not want to be in a supervisory role towards a family member. In that role I need to be able to make unpleasant decisions, like tell someone if (s)he did a bad job, handle complaints, or even discontinue employment. That is hard enough as is, but if it involves a family member...