We stayed at the North Rim campground inside the park the day it opened on May 15th, and drove past Jacobs Lake. Jacobs Lake Campground appeared to be a nice place, with tall trees, and fairly clear sites. Our Discovery is about the same size, and we too towed our car. I would have no concerns staying at Jacobs lake. Reservations inside the park fill up fast, but if you want to check it out, there are sites that accommodate rigs our size with no problems - see pix below. Enjoy - it's a beautiful park! And yes, it snowed on us the day we arrived...
Joe and Debbie, Emma the Aussie Cattle Dog who adopted us
2012 Discovery 36J, Blue Ox and Air Force One, 2010 GMC Acadia Toad
USAF (Ret) WDØM http://wd0m.com