Good luck on your trip to the Fort. Here are a few tips I can share for a long trip.
You are traveling with a travel trailer which is what I do. I haven't slept in a wal-mart or similar situation. I might feel more comfortable doing that in a Class A or C, but not in a travel trailer.
I plan for about 500 miles per day as a very long day. I have done more, including an 800 mile day, but wouldn't recommend it if possible. That is with two drivers switching off every few hours. We drive at 60 miles per hour, which is the max recommended for the trailer. We stop in rest areas to have lunch and other breaks. Plan on every stop taking a little longer than you would expect.
KOA's usually make a good stop for a night. There are other similar campgrounds that can work. Look for something close to the interstate and well rated. RVparkreviews.com is a great resource. On the way to the Fort, I have used the Savannah South and Fayetteville KOAs and can recommend them. While I really like camping in state parks, they often have 2 night minimum stays or other restrictions that make it hard to use them on a trip like yours.
As for unhitching, you should be able to spend the night without unhitching. Having a level, pull-through site really helps. In the morning, you can just unhook the power, water, etc. and head out.
Hope you have a great trip.