OP you have my sympathy. There is 5 years between my second and third. At roughly the same ages as your two are now I also had to deal with them constantly bickering and scrapping - although not to the extent of damaged eye sockets and choking. Every living second of being with them began to feel like living in a battleground.
One day I simply broke down and told them how it felt to live with them. How it felt to have failed as a mother and that I couldn't put up with it any longer. I asked them each why they felt they had to be at each other's throats constantly. I gave them time to think about it. It turned out that even though their initial response was "I hate him/her" when questioned they didn't know why they hated each other. I suggested maybe it was just a habit they had grown in to.
Anyway to cut a long story short I laid it on the line and told them I was no longer prepared to put up with it. They were causing me to not want to come home from work, as home life was becoming increasingly uncomfortable, and if it continued I would be leaving.
They were shocked! But, immediately, their resentment of each other became less and less. I prepared activities for them to do together so they had to rely on each other.
It wasn't all plain sailing and there were times I had to remind them...even a look was enough to stop them in their tracks.
Now aged 32 and 27 they are the closest of my 4 children.
There is a solution. You just have to find it. It's not easy when you're so bogged down and can't think clearly.
Please don't suggest your dd moves out. Talk to them. Let them come up with their own solution. They need to know how their behaviour is affecting you. Everyone needs their mum and most will do anything not to lose her. Chin up sweetheart. It's time for a heart to heart with them. Lay it on the line and don't back down. Be calm but forceful. Wishing you all the luck in the world xxx