Thanks to not looking at the map on the way back but relying on signposts, we ended up missing the turning from I-10 back onto I-49 and went about 80 miles too far along I-10 ending up in Westlake, LA. Instead of going all the way back to Lafayette, we turned north onto US-171 and then cut across back onto I-49. In all the whole trip back was about 8 hours long in spite of the wrong turning.
Texarkana to New Orleans is roughly a 420 mile journey which should take (according to mapquest.com) 7 and a half hours.
Lori and I left the kids with her family and did the journey on our own. Although quite a lot of the tourist attractions in New Orleans are the kind of thing that they’d like, the journey there is a bit much by car and hotel accommodation for all of us would have been quite expensive.