Ah, so you're still on the hunt!
By late October, the weather here in Texas and across the South should have come down from "inferno" to just "warm" so you've picked a good time of the year for your visit.
Personally, I never found much of particular interest along I-10 between Houston and Baton Rouge. I'm sure people who live along that route may have some good recommendations for places to eat, though. You'll find that I-10 through there is a long chain of bridges strung together with chunks of land. (This is an exaggeration, but the closer you get to New Orleans the more it seems that way.)
The State Capitol building in Baton Rouge is somewhat unique among state capitols in the US, it's a skyscraper instead of the typical dome between the 2 houses of the state legislature.
New Orleans itself, of course, is a must-see and a very unique city. If you happen to be in New Orleans on Halloween, the French Quarter will be very wild and it might not be a good place for your daughter, so that might be a reason move your New Orleans stop forward or back on the calendar. I went to grad school there, but in the early '90s so I'm sure I'm not current on the best places to eat anymore.
Are you just planning to inspect any likely candidate trailer on sale near your route?
Zero Gravitas — 2017 Flying Cloud 26U | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill