It looks like you are dealing with some of what I am dealing with on the left side of my driveway.
Suggestion and only my opinion:
If you have anywhere on the property that you can steal some dirt from, fill the holes where water sets and drive over it several times to pack it down. Then let settle for a few days and do it all over again. Once this is done and the water starts to shed away from where you plan to drive, have the rock delivered then and make a crown so the water will continue to shed. Use a large rock base 2-3" rock and smaller on top of that. The larger rock will settle into the clay, which is what happened for me. Clay once compacted will hold hard as long as it have rock in it. If it doesn't have rock in it, it will get slicker than snot!
:2cents: