I have this problem with exhausted families as well, and play them generally only from about 5:30 pm to 9 pm. With that usage it irritates me that they are ALWAYS exhausted.

Last night as soon as I logged on I fed my peeps as they were all exhausted and half fed. I then let them all sleep a cycle...which brought them to tired...they then napped or slept a cycle again, and that brought them back to elated. It's a pain, but it appears before I can do anything with them I have to immediately feed them and put them to bed, and then after 30 minutes to an hour of that I can finally work on the game with them.

Oh, and yes, I put them all to bed and praise them for it before I leave. It doesn't seem to matter as by the time I login again they've all gotten promotions and such. Obviously they're inclined to work rather than rest while I'm away.