I agree with the others. I just finished a gig as a campground host, and counting heads was NOT one of my duties. I, too, much prefer to camp next to a family of a dozen that manages to get quiet when quiet hours come, and who behave more or less civilized vs. even two loud drunks.
Every institution has rules that are essential for proper functioning of the whole, and rules that are there primarily to be pointed to when a problem arises. Number of campers per site is one of the latter. I'm astonished the lady you talked to would take that position, but so be it. There are other campgrounds, and when asked how many folks to expect, just say "oh, just me and the wife and our kids." It is NOT their business to limit the size of your brood.
But there are campgrounds more or less kid friendly, as there are ones more or less dog friendly.