@IdleBrick It's a difficult topic, as there is no ultimate solution. Pretty much everyone had came up with own ideas.
My good looking solution was to separate the physics and visuals. Because of the high frequency that I use (1000Hz) I don't have to care about jittery movement, because it's so fast it looks stable.
The only problem was with wheel angular velocity, it looked like crap. So I made a second variant which was smoothly blended toward the one physics gave out. Thus wheelspin lagged behind physics but it was not visually disturbing. The only bad thing with this is the oscillation of angular velocity goes back to the engine. Fortunately when it starts to happen the engine RPM drops so the engine stalls.
Some relaxation method uses damping, that mimics the characteristics of tension accumulating in the tire, and releases as it rolls (or something like it) ?
They usually have the downside of the car can slide down on hills (even sideways).
A quite old paper SAE950311 that is sold for $20 or something deals with this topic. I bought it, but didn't work out for me, so I don't recommend it, but you can give it a try…
Yet an other approach is to have a separate simulation model for low speed (which is not perfect at high speed) and just switch or blend between them.
btw: The cornering stiffness is not something that you need, just like horsepower. They look cool on charts but in simulation you only need forces and torques. Nothing else.
And different coordinate systems that are very important. Most components are simulated in their local space and the conversion between those is essential.
I recommend you to dig through the sources of Racer (racer.nl) in case you haven't done that already. There are lots of interesting ideas in the comments too!
I don't remember if we talked about your simulation FPS. If you use the rigid body simulation of a generic engine, there is a bad news… there is a light chance it's not gonna work (especially at low speed) unless you crank it up to to at least 200-300FPS. There are solutions like PhysX's Vehicle Controller which also runs at high frequency in the background, and syncs the 2 separate simulations. This is also what I do.
For some extra info search for REC.AUTOS.SIMULATORS google group (what you may need is somewhen between 1999-2002)
The guys who later made Test Drive Unlimited or Assetto Corsa faced the very same problems, 20 years ago ?