Why should your father or brother do anything? The fact that your brother voluntarily did the dishes is amazing--reward that behavior! But your dad? If he's been waited on all his life & thinks that's fair, he won't change without sufficient motivation. You might have to get him to trade chores. You'll cook if he'll vacuum, for example. Worth a try?
The exhaustion, for me, is the hardest part of depression to deal with. No meds have helped a bit with that in my case.
Keep coming back here, and never worry about the frequency or length of your post.

all you want. We each get our turns at all of that--part of PsychCentral's continuing charm!