I don't know the exact routing you have in mind, but I am going to make the assumption that whatever route you take, you will pass through Amarillo. My advice is to skip Dallas, instead take US287 to Wichita Falls, then US82 across to Texarkana and I-49 down (this actually shaves about 20 miles off the distance, and lets you skip the DFW traffic). US287 and US 82 are good roads, and for the most part 4 lane, much of it near interstate grade highway. For stopping to spend the night many smaller towns in the Texas panhandle have low cost or free campgrounds with hookup, we stayed at one behind the chamber of commerce building in Andrews, TX last fall, 6 water and electric hookup sites with dump station (big new concrete parking lot), which was free for up to 2-3 nights. Also there are some BIG rest areas along U287, and overnight parking is allowed in all Texas rest areas.
Once you get to Shreveport you will probably want to take the I-220 / 3132 loop around to I-49 heading south (I-49 is not yet complete through downtown Shreveport), the loop north of I-20 is the I-220 loop, south of I-20 it is the 3132 loop, which is interstate grade, but some people in RV's have issues on it due to the expansion joint spacing causing resonance with axle spacing, if you have problems just slow down a bit, it gets better after about 5 miles.
Now I will ask if you are sure you want to go through Baton Rouge, and if you do I STRONGLY suggest you try not to hit it at rush hour, or more like rush HOURS, which extend from about 4-7pm at which point in time traffic on I-10 from the Mississippi river bridge to the I-12 junction tends to be gridlock most weekdays. Now if you do go through Baton Rouge, do take I-12 across and miss New Orleans this cut off saves many miles of driving with one end at I-10 in Baton Rouge and the other end at I-10 in Slidell
