For someone who feels "nothing", you are sure going to a lot of effort to get your T to "get rid of" you and you also explain that expressing your feelings is hard. It should not be hard to express nothing and I cannot imagine putting in a lot of effort for it either?

Useful things aren't "living". Yes, the kids need you, as you, but you need yourself too and not just someone going through the motions of being a mom, house cleaner, gracious daughter and sister, etc.

I would make a list of 25 things you "could" do (that don't have anything to do with your life/chores now) and then pick one and try it. Or, I would pretend you have several million dollars and think of specific things you would do with it and then figure out how to start on those things with a little less