I've been there. It was the hardest thing I've ever had to do so I know a bit of what your family is going through. Know that you're doing the very best and right thing. Right now it hurts like hell but in the long run you can only help those that want to be helped.
In my case that family member needed what I did to some time later finally get the help they needed. I will pray for you and your family so that all turns out well. Know there is hope.