You haven't failed as a mother. He has failed as a son. With every action comes a reaction. There are consequences for his actions. I say pack him up and ship him out to dad's. The key for you would be to not take him back unless there is some kind of substantial change in his behavior over time.
He is 16 and should bare much of the responsibility for his actions. You don't study you get bad grades. While having ADHD, makes things difficult, you should make better choices.
Not all students fit nicely into the mold of what traditional school looks like. He may be better served having a different kind of learning experience by being in dad's house.
My sister was just the most aweful child ever. She was socially promoted through grammer school and eventually dropped out of highschool. My mom felt like a failure but she was a great mom to both of us. She did the best she could do but my sister never did the best she could have done. I can't even tell you the amount of tears my mom shared over my sister or the depth of a sense of failure she felt too. My mom spent so much energy and effort on my sister that I was left to basically fend for myself often. I'm the oldest and it would have been nice to have had my mom's time and energy too but once she was so consumed with chasing after my sister and dealing with her drama there wasn't much energy or time left for me so I made due. There wasn't a thing my mother wouldn't have done for me. She loved us both but my sister was so very difficult and required so much more.
My mom didn't have an option of sending her to dad's like you do. When my sister finally moved out it was glorious, like the dark cloud had lifted.
There is no doubt in my mind that you are a great mom. Your kid is just aweful and he will have to learn how to live with the decisions he has made. He can live with his dad for the next 2 years and then he will be a legal adult and you are legally off the hook even though emotionally you may feel like you need to help him. Perhaps the best help you can provide is by letting him get to the bottom of himself and stop treating you like you are the enemy.
I hope this helps.
The only person you can change is you and you should allow anyone to mistreat you even if that person is your child. It also will be good for the other kids to see.