Your DH seems a bit controlling and his behaviour is verging on the unacceptable. You do not need to ask to get out of your own car, surely! What is 'the look', moreover?
My DH is inclined to be a bit of a bully when he gets behind the wheel but I always let him know I am up for a fight if he is! Mostly, I let him get on with it and just enjoy the free chauffeuring but if he gets tetchy with other road users I usually say something for safety's sake.
However, we are usually in harmony and have quite an effective parking policy. Like you, we know that spaces in full car parks become available frequently so we lurk at the entrance to a parking lane and wait until something is coming out, drive up to it and signal to go in to alert others of our intention. In really busy times I get out with my phone and walk round the car park. If I see a space coming up I go and stand in it and wave and/or phone to signal where I am. The DH then drives to the space.
Bonkers, I know, but it works and beats waiting and getting frustrated.