Hi Adam,
Hope the therapist is helpful. To me, it is not a real dilemma taking more care of yourself (even if you need to enter a hospital to be better) vs. taking care of the baby business. Without you there is not parenthood for you. Because of my cultural background, I read your lack of care of yourself in a different way: I don't see much as a consequence of your depression but as something radical in your inner self, that is fueling your depression. Perhaps you have not been taught to love yourself properly. This happened to me and many others I know, that are busy thinking of the future and how we will not be able to take care of others while we are falling apart. I really hope you can focus on the present moment and how you can be better, you deserve it, Adam.