Is there a way to get at least some control over the cars with just mouse and keyboard? All I managed so far was breaking off fences and roadsigns and ending up facing in the wrong direction. Oh, and once I drove my motorbike off a cliff..

Assuming you have the Gentlemen of the Row mod, even the handling mod within it doesn't seem to be enough.

Using this one and adding it to the GotR compiler should do the trick.

Hm, no real help there, but thanks anyway.
Maybe I get the hang of it if I try for a century or so. ;)

What I can tell you, then, is to make the most of cruise control. Accelerate to a reasonable speed, then use the cruise control hotkey to maintain that speed, and increase/decrease it peacefully as needed.

it seams that on some computers sensitivity is off, like : mine win8.1 ok (bit more sensitive than gta5), my brother win10 ok, friend win 10 bit to sensitive, other friend win 10 same as gta5
also it maybe have something to do with framerate, as i am runing it at fixed 30 fps and have no problem switching between gta5 and saints row 2 driving (gta 5 performance video settings, sr2 max quality)
tho saints row 3 have more of gta4 sensitivity or slower (both max quality video setings)

Still rather difficult even after hours of training because it's nearly impossible to make minor adjustments to the direction. But if you take the whole town as a demolition derby it's kind of fun...;-)
Well, sometimes it is easier to steal a new car than getting the current one out of the ditch or mass accident you drove it in

I play SR2 with Keyboard+Mouse only. I have some tips regarding car driving:
* Do NOT enable "Sticky Camera" in GotR, so you can focus on actual driving rather than camera controlling.
* Use Handbrake (Spacebar) wisely. Sometimes it is better and cooler than simply slowing down using brake (S key).
* The handling and the difficulty of driving differs heavily with the vehicle you're controlling. Try to steal and test many different cars and find the best one that suits to you. My personal favorite is the police Cruiser, but your preference may differ.
* Upgrade your cars at Rim Jobs or Semi Broken, so minor scratches and crashes will become less of a problem.

I got tired of struggling with the controls while driving on my PC, so I decided to get the game on Xbox instead for $2.49. It works much better on the Xbox. No crashes or glitches and additional dlcs are available for purchase.

I also was able to get the first game Saints Row 1 on Xbox as well since it is an Xbox exclusive.