There's a lot of good advice above.
Personally, I'd think there could be more danger with a vehicle hovering behind - inattention of your driver could be a factor as well as dangerous overtakes. There are some crazy speed limits in Texas!
What's not clear is your level of experience?
Have yourself and your son done multi-day tours before? Are you both happy riding at the same pace? If not, that could lead to difficulties, especially with a support vehicle bringing up the rear.
If you have experience, is that with the support vehicle behind? That is something you could practise beforehand. I'd imagine the SAG driver especially needs to practise. Hours driving at a slow pace is not easy.
The thing with fear/anxiety is that it is often irrational and therefore difficult to control.
As a European, I found a mirror invaluable on US roads. There were drivers who were ignorant of their impact zipping past at high speed, those that were just malicious (few, but they existed) and some who were quite unaware of their loads (think wide trailer behind a pickup).
I came to hate bridges! A shoulder, if it existed, was often full of debris. I can't imagine a slow moving vehicle being particularly popular on some.
The best way of answering these types of questions are to get out there and do it, preferably close to home first.
You could do a search on CrazyGuyOnABike for people who did similar.
As for laws, you'll be crossing numerous states and counties. Irrespective of legal or not, there will be roads at certain times where you will be very unpopular!
Good luck!