I know your mom lOves you and is trying to think of ways to help but writing letters like that to your family when you are in such a bad places sounds a bit triggering to me. Too much like goodbye letters. I like the letter you wrote for the Pdoc it explains the current state of things well. The time since you last saw your friends mother doesn't matter, nor does the rational part of the brain that tells you how bad your passing would be for your family, Sui has a way of triggering the emotional brain for those in a bad place. iP or IOP would be a great place to process the feelings, the emotional response to a death that hits so close to home.
Take care, MM is right you are worth much more than the cost of day care.