Aside I'm not much an expert as well but, from DC to AC we are pretty efficient, around 98% of energy get converted. But the other way round it's pretty inefficient, meaning a loss around 30%. So while your p.v. it's pretty efficient in generating AC, your car it's pretty inefficient generating DC from AC to recharge. You heat pump would gain as well.
To be clear I do not advocate DC for any DC home appliance like washing machines or dishwashers, just for energy intensive appliances like big heat pumps and car chargers. Not more.