It seems to me that a water reservoir with a tube going near the engine (for heating) and a small water pump, coupled with an inflatable bathtub could solve the shower problem.
I've never lived in a van, but my family used to go camping and we used a similar system (inflatable bathtub inside the tent) so that my younger brother could take a bath even if it was too cold outside for him.
It's far simpler than that for most of the year, solar powered showers are $20 and work really well (often, too well, I've been burned by one camping).
I've never lived in a van, but my family used to go camping and we used a similar system (inflatable bathtub inside the tent) so that my younger brother could take a bath even if it was too cold outside for him.