Those of us who've never seen your property cannot gauge what you're describing, or appreciate its important details. You'll need to provide a picture or two.

Here's a very rough sketch of the layout. The proposed spot for the turnaround is labeled "new". My major concern is how to layout an adequate turn radius from the turnaround to the driveway because the "inside" curve of the driveway is a short retaining wall that must be avoided.

The sketch helps me grasp it better, but not a lot. This is a project for which you may or may not get good recommendations via this thread/forum. It's likely that the "devil will be in the details." Inches might matter. If you want the best recommendations, it would be better if you come clean with the most amount of information you can offer: a diagram that is measured (to scale) and/or photographs that show the problem, the conditions and the setting. If you were hiring someone local to provide professional expertise, you certainly wouldn't expect them to provide a solution based only on the information that's presented here. It's possible, too, that you might get suggestions for solutions you haven't thought of. Since it's not just a plant-a-little-bush project, it would be to your advantage to provide better information.

Based on the above sketch, the only thing I can offer now is "don't get the turnaround too close to the house to allow for adequate plantings. Keep it at least 6' to 8' away... minimum. But that's information is provided pretty much in a vacuum.

Can a car presently be driven into the space marked "New," or is there stuff in the way? If it were my place, I'd be inclined to do some experimentation with the car in order to gauge what can be comfortably done. And then add some width to it so that it is really comfortable when all is said and done. Rarely does anyone ever complain from having "too much space." It's almost always the opposite.

It will depend on your current driveway width. If it is a single width driveway (often 11' in my area), you'll need more width to the hammerhead than if you have a wider driveway. I typically make a hammerhead for a single width driveway a minimum of 14' wide and 20' deep with 10' radii.

Keep in mind that you now have to deal with what happens when you park multiple cars and someone has to leave. You may want to consider making the hammerhead wide enough to park a car or two and be used to turn around - perhaps making the two parking spaces and using the driveway as the turnaround.

If the driveway is wide enough for 2 cars, you can narrow the hammerhead to 11' and cut the radii to 5' with a depth of 20'.

These are minimums, although you could get away with a little less than a 20' depth if you are only turning around.

PS - why can't you just reverse the direction of how you use the driveway?.... drainage issue?

Great info and comments. The drive is 11 feet wide at the street and widens out as it approaches the portico. I've done some chalk and tape experiments at a local parking lot and our cars will easily navigate a 18' D x 10' W hammerhead with 5' radius and there's room to make it deeper. We gain some advantage from paving the wedge area between the hammerhead and portico. And we don't plan to use it for parking while there are two cars in the portico the curve on the house side.

We can't reverse the direction and use the other side due to the grade; the side to the left of the diagram; is VERY steep; about 25%. It's completely blind and we've had two incidents of cars sliding backward and damaging the house wall when icy (frequent in winter. It's not long enough to reduce the grade. The other side is about 10% and a straighter approach. We are on a loop road and always leave and return from the direction to the right.