Flexible travel, short notice flights?

[78F350]

In a week or two I plan to drive a car (old Audi A6 Avant) from Oklahoma to Phoenix and give it to my daughter. About a 1,000 mile drive. The get in the car and drive part is easy. The get back home part is what I am trying to figure out now.
I don't want to buy an airline ticket much in advance because I haven't determined my exact travel dates. My daughter is about due to have a baby after a difficult pregnancy, just bought a new house, my grandson is about to start school... It's hard to know if it's best to make it a short overnight visit, or stay for a week. I'll know when I get there. Flexible travel plans are my goal.

-Can you walk into an airport, buy a ticket and go for a reasonable price with no advance purchase? I know I have had to make short notice changes for canceled/delayed connections enroute and it was pretty simple. Are there actually good bargains to be had with some flexibility?

-I could buy a cheap car to drive back home. Maybe sounds like a bad idea to many, but I buy about a dozen cars a year to strip, flip, sell, or give away. About $2k cash, a tool bag, fluids, and a credit car for contingency... I could have some fun and enjoy the risk and adventure. This is a solo trip while the wife stays home with the dogs.

-I could ship the Audi and drive a Boxster. Somehow that just doesn't feel right. Part of the purpose of the trip is to 'bring the Audi'.

-I could drive a Cayenne and tow the Audi on my trailer. That's a lot of trailer miles and a lot of gas and wear running the Cayenne with a heavy load. Empty trailer coming home..?

Do you have any Travel tips, advice, warnings, or stories to share?

A few internet searches as I wrote this have shown some decent samples of last minute airfares.