You have children. You are responsible for them. It is up to you to feed them, educate them, etc. If they have a problem, it is up to you to address it in some way. You are responsible for them.

You are not responsible for the feelings of others. So if your husband is depressed, it is not automatically up to you to make him undepressed. If your mother is annoyed about something, it is not automatically up to you to make her unannoyed.