Call me a tree hugging hippie if you want (you'd be majorly wrong though), but this idea that you stake a piece of your club or own it for the day just sounds drunk to me (I'm refraining from using the tone/exact words needed to describe the feeling).
For example, how many of you have belonged to a boating club with your trailer boat? .... when you use the club boat ramp, you use it to get your boat in or out of the water, then clear out to let the next guy in line have access, and if you don't make way often enough and hog the ramp all the time, it could cost you your membership. Don't know about you, but picking up your plane and letting the next guy in sounds a LOT easier than moving a couple of tonnes of car and boat!
All I can say is chill, get over yourselves, let others have their turn, and hey, at worst, you helped someone out, and at best you might get to know someone new! Paying your dues/fees at a club entitles you to belong to the group and share the facilities, paying your fees does not generally mean that the club hands over the ownership of the entire field to just you so you can sit around saying "mine mine mine"!
Live and let live I say.