We were in Sequoia a few weeks back and once you enter the park on Hwy 198 there were signs saying large vehicles not recommended. I think the sign listed vehicles no larger than 24 ft. I wouldn't consider pulling a 31 ft trailer to Lodgepole from the park entrance on Hwy 198.
We stayed just outside the park entrance in Three Rivers. It was just okay, if I were to do it over again I'd stay a little further away at Lake Kaweah. Most of the sites are not full hook up but they do have one saved for a camp host. We stopped in and they said if that one is not taken you can have it. So if that interests you give them a call. Some of the other sites might also be okay, depends if you are looking for full hookup or not. Mid week the place was empty, different story on the weekend though.
If you are in this area check out Mineral King, and go to the very end. It is a windy switchback that is 11 miles but once you get there it is worth it. Don't take your trailer or large truck, but short bed or non dually okay. If you go get the story about Disney and Honeymoon Cabin.
Another option would be to explore Hume Lake Campground and surrounding area. It's at the north end and you would enter the park up there, not down at the south end, it looked like a windy road (Hwy 180) but I saw some 30 ft trailers there. Nice area...
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