As a military retiree, my spouse does not need any pass for base access, she has her ID card.
We have stayed at two Air Force FamCamps; at Malmstrom AFB in Great Falls, MT and at McChord AFB near Tacoma, WA. Neither required reservations. In fact, reservations can not be made at Malmstrom, first come/first served only. The campground is not on base.
It was many years ago that we stayed at McChord, so I don't know what the policy is now. At that time, we had no problems with base access. The campground is on base.
How the campground is administered is often up to the local command. That includes who is allowed access to the campground. The Pass policy for your spouse may be a local policy, or it may be DOD regulation, I don't know.
If I were in your situation, I know I would never again patronize any military campground unless it is outside the fence as the one at Malmstrom AFB is!