Can I ride through unoccupied carpark spaces?
AFAIK there are no road rules requiring you to give way to traffic behind you when travelling straight down the road, ie, not turning and not at any intersections.

Riding over an empty carpark space is also completely legal and normal.

There are places where one must not ride more than 2 abreast, and some locations have rules about impeding lane flow, but you're not describing that situation.

You've simply met an impatient driver, not much you can do for them.  Have patience and tolerance.