Your website is great! Tons of Information! I use an older Hennessey Hammock most of the time, and love it - but I can't sew very well.
You won't have any trouble with Cone Peak road in your jeep - as long as the road itself is open. Always check with the FS to make sure. If you can haul her stuff for a mile or two, Fresno Camp on the San Antonio trail isn't very far - just a pain coming back up the hill, or Forks camp on the Arroyo Seco Trail - about 2 miles in, but the trail's in great shape.
If you can get another family with kids - then car camping at Memorial campground can be fun and you can usually have a large area to yourselves in the winter. Like Mark said - you can have a backup plan of camping almost anywhere on del venturi road.
hth
dbk