I work at a charter school connected with a boys home, some of the boys are rehabbing when they first arrive so I can speak from the other side. Your teen will be angry, will tell you that nothing is working and they hate wherever you sent them. They will tell you horror stories of how they are being mistreated and ask you to please let them come home. Don't do it. If you had trust in this facility, then please listen to the professionals and don't give in to your teens requests. I have seen it over and over again, the teens all, 100%, no exception ever start out this way. Over a period of about 2 weeks to a month, they settle down and that is when the hard work can begin.
Hang tough and like the other posters have recommended, get some counseling for yourself. Life will need to change drastically for the entire family but it will be worth it in the long haul. And I am not blaming you or your home for the situation, just know that some hard truths have to be examined and changes will have to be made to keep your teen clean and sober.
Prayers