Hopefully someone will be able to weigh in about the current conditions (or, at least, more recent info) on the Death Valley-Big Pine Road (which is, I believe, what it is called on road signs on the Big Pine side).
The first, and only, time I've been on that road was in December 2013, in a Farabee's rental Jeep. The washboard was terrible, and there were some washouts that were nasty because they were very hard to see, up near Crankshaft Crossing, but those might be further north than you're planning on going (one particularly bad one I hit at just over 30mph and felt like if I'd hit it any faster I could have lost control of the Jeep, which freaked me out a bit and I drove the rest of the way really slowly).
Other than that, I recall the road being in good condition compared to the Racetrack Road; like Taco said, it's more of a unpaved country road. So my biggest concern about a rental sedan would be the washboard and deep, hard-to-see washouts. If you do try it, be sure to take it slow and carefully, and have a tire repair kit.
In regards to parking, my immediate thought (without measuring distances) is that you'd be parking near to the old road to the Skookum Mine (should be able to see the old road on TOPO maps, probably also Google Earth). If so, I recall from Steve Hall's trip report that there was a good parking spot at the start of that old road, which hopefully will also work for your planned hike.
The first, and only, time I've been on that road was in December 2013, in a Farabee's rental Jeep. The washboard was terrible, and there were some washouts that were nasty because they were very hard to see, up near Crankshaft Crossing, but those might be further north than you're planning on going (one particularly bad one I hit at just over 30mph and felt like if I'd hit it any faster I could have lost control of the Jeep, which freaked me out a bit and I drove the rest of the way really slowly).
Other than that, I recall the road being in good condition compared to the Racetrack Road; like Taco said, it's more of a unpaved country road. So my biggest concern about a rental sedan would be the washboard and deep, hard-to-see washouts. If you do try it, be sure to take it slow and carefully, and have a tire repair kit.
In regards to parking, my immediate thought (without measuring distances) is that you'd be parking near to the old road to the Skookum Mine (should be able to see the old road on TOPO maps, probably also Google Earth). If so, I recall from Steve Hall's trip report that there was a good parking spot at the start of that old road, which hopefully will also work for your planned hike.
Link to my DV trip reports, and map of named places in DV (official and unofficial): http://kaurijacobphotography.yolasite.com