You may find that even the park model itself needs a permit. Even rural counties typically have restrictions on additional housing placed on a property.
You can skirt the issue by "storing" an RV on the lot and avoid telling anybody you plan to use it as an apartment from time to time. That probably doesn't work if you will stay there full time - sooner or later it will be noticed. Add water & electric hook-ups and run a temporary line to dump into the septic when needed. Easy if downhill, or add a macerator pump is flat or uphill. I do that at my own stick house, so we can use the coach as a guest apartment.
If you are planing on living at your parents lot for an extended period, check with the county on on requirements for placing additional housing, temp or permanent, on the property. Then decide how to proceed.