I used to drive with keyboard, starting from F1C then to rFactor.
I then tried GP4, and it was a completely different experience. I didn't have to do any work while driving - on rails basically. Basically all I needed to know was how to accelerate and when to brake, no real turning knowledge needed. So if you're coming from there and you're used to that feeling, I assure you that you will need to learn to drive, period.
I've since switched to a wheel, and for sure the driving is better. But if you're like me who had to wait a number of years before being able to buy a wheel, I advise you to simply practice driving, as its the best way to get used to a new game.
And now to answer your main question:
there is no F1 mod in rFactor that has the type of handling that you're looking for. It's not the mod that's causing you to spin, its probably that you're used to GP4 and driving on rails. So again, just try to adapt to rFactor slowly by practicing. Try driving slower than you might normally and focus especially on keeping the car on the track and facing in the correct direction (if you're always spinning, which I take it you are).