Donnie, I had that exact thought yesterday. I found one of my son's beat up RC cars and opened it up. Right off the bat it became obvious this won't work. Well, not without further tinkering anyhow. Problem is the motor is way too fast and I'd need to add something to the mix to slow it down. For a moment I was thinking, what if I disconnected the motor from the car and replaced it with a motorized pot from an old Yamaha receiver I have sitting around.
I scrapped that whole idea and ended up ordering two devices similar to the one that EdwardGT posted. Two of those came out cheaper than one Arduino build I was considering. Going to take 2-3 weeks to get the parts, once I get them and have some time to tinker I'll share the results.
During my search, I found this. It's definitely not cheap, but for someone who may not have the patience or skill to build their own it could be a good option.
https://www.etsy.com/listing/1136750919/vintage-audio-remote-volume