Oh, my dear Steely...
I can not fathom your pain, but I know that you can go on because you must. difficult child needs you. Your sister needs you. Your family needs you, tho they may not know it right now. WE need you.
Time will help heal your pain. Tell yourself that until you begin to believe it. For a while it will seem like you are nothing but a robot, going thru the motions. But the burden will lighten; the pain will lessen.
So many, many hugs and prayers being sent to you and your family. Know you are loved and others are sharing your pain.