I cannot agree that the kids will forget you. My God daughter has seen me for the first time in two years, she's only three. She remembered me. They will remember you, but it is your choice to dictate how they will remember you.
Leave them fond memories to hold onto if you decide to go through with it. Leave them a letter to remind them that it is not their fault, and that you love them.
Do what you need to in order to settle your heart. You have been through enough, and no one has the right to take your choice away here, like they have with other things. Seek help from a psychiatrist, not an er or a primary care physician. If they liken your pain to a pity party, leave them behind and find someone else to talk to. You don't need that negativity on your plate.
If you decide to exit, look for methods that minimize impact on the munchkins. Cleaner methods, less blood, away from home. The last gift you can give them is not to traumatize them more than necessary.
Remember, it's your choice. It's your body, your life. You are the only one who can decide what is appropriate for it.