I drive from central Texas several times a year, mostly by myself. And I’m old!
The trip for me is approximately 18 hours, not including stops , so I break it down into three 6 hour segments. I used to drive 9 hours the first day & 9 the next, but have discovered the 3 day drive is much less stressful for me.
I’m not sure of your route from Austin, but the best advice I can give you is to avoid Houston! I go through Bryan, to Navasota, through Montgomery/Conroe to Beaumont. I think 105 is the road I take after Hwy 6.
When I did the 9 hour split, I would stop in Biloxi, staying at Beau Rivage. If you do the 2 day drive, you’ll get into Disney late, especially since it’ll be an hour later there.
The way I go now, I stop in Lake Charles ( stay at Lauberge), Crestview Fl ( either Country Inn, Holiday Inn Express or the brand new one-whose name is escaping me right now!)
The only hard driving is through Baton Rouge. Lots of traffic, semis, merges, & lane changes. It’s not so bad traveling east, but much worse going back west. So bad, in fact, that I’ve found a different route that skirts around Baton Rouge. Takes about an hour longer, but worth it to me!
I just returned from Disney & had my 11 year old grands with me. They spent the travel time playing on their iPads, snacking, sleeping & listening to music. There’s a great pool at Lauberge where they spent a few hours swimming. They complained very little & they’re very used to flying most of the time.
Just be sure you’re a member of AAA or the like & don’t let your gas tank go below half empty & it will be a great road trip!