While I think some of the rules could be "less strict", I absolutely, 100%, believe that the time to ask for an exemption to the rule is BEFORE you break it.
In this instance, doing as the OP did and explaining his circumstances and asking for a waiver of the "6 persons per site" rule was fair. The park then had the option to make an exception or not. No harm done on either side.
If the park had waived the rule, the OP could stay there knowing he wouldn't be kicked out; because the park didn't waive the rule, the OP knows it wasn't a "large family friendly" park and he would be better off going elsewhere.
Same with dogs, generators, alcohol, etc.
Ask permission not forgiveness.