Earlier quoted context omitted.
In other words: please go home and I'll call you. 'Head on home' is a real expression. Similar ones are 'head over there', 'head to ...', all of which just mean 'go to'.
I mean more the "Why don't you ..." It's quite obvious that it's rethorical but it seems so nonsensical to put this into a question while camouflaging what is really going on.
Both people presumably do know what's really happening, and this is exactly why it's seen as unnecessary (and inconsiderate) to actually say it. There's no reason to call extra attention to something unpleasant.