I think it is very much time to call the psychiatrist and ask about hospitalization. She tried to kill your easy child. Plain and simple. Whether she is "over" being that mad or not, she did it. Violence cannot be tolerated. Once she has done that she will most likely try it again. Possibly with tragic results.
Your easy child MUST be in counseling so that he can learn that he truly does not deserve to be treated that way. The local domestic violence center can help with that. Sibling violence IS domestic violence and IS something they help with. You may want to look into some of the books on Sibling Abuse. They can be very helpful to you as a parent to help you find ways to protect the kids.
You MUST have a safety plan. Period. Put it in writing. Post copies around the house and make SURE that 911 is posted on the phone because kids forget what it is in emergencies. EVERY handset should be labeled. You should role play calling 911 with easy child so that he CAN call for help.
Choking someone can damage their throat, spine, vocal cords, etc... It does a LOT more than just cut off the air. Repeated choking can cause scarring on the arteries and veins that handle blood flow to the brain. It can create lifelong scar tissue that will be a problem as they get older. (I know because I experienced it as a child and because my daughter went through it with Wiz).
You may need to have easy child checked by a doctor. If a doctor or teacher sees red marks or any lingering signs of choking they MUST report it to child protection services. Just because another child does it does not negate mandatory reporting. They will want to see the written safety plan, and see if easy child has a safe place to get away from difficult child. Sadly if CPS thinks you have not handled it properly or will not handle it properly they will NOT take difficult child. They will remove easy child. It is FAR easier for them to find a placement for a easy child than for a difficult child. difficult children are expensive so CPS will try to leave them for you to handle, even if the difficult child is terrorizing the family. been there done that on that also. I was appalled at the idea they would take both my younger kids and leave difficult child with me rather than helping all of us or even just helping get difficult child services. The written, posted safety plan will be an important thing to show that you are not taking the situation lightly.
Have you taken photos of the marks on easy child? In the future you NEED to do this. Bruises may not show for a few days or a week, depending on how deep the damage is. Jess takes at least a week for bruises to show, so it can take that long.
PLEASE try to get the psychiatrist to help with the aggression. some medications can help (antipsychotics like risperdal, abilify, geodon, seroquel, zyprexa are usually used).
It is NOT your fault that difficult child went this far. It IS your job to take immediate steps now that you know she has done it once.
I am sorry this sounds so harsh. I know it is scary to think that difficult child might have killed easy child or caused lasting damage. I know because my difficult child did it to Jess for a long time before I found out. She hid it because he threatened her.
It IS scary, hard to wrap your brain around, and hard to cope with. there are lots of threads about safety plans in the archives. I think they will be a great help to you.