you can tell that the plane is not completely under the perfect control of the cockpit
This is a mistaken belief that perfect control equals perfectly flat and level.
Driving down the road, you will frequently drive over a pothole and have the car judder briefly. Driving down a track, you will probably find more frequent shaking of the car. Driving offroad, shaking is virtually guaranteed. None of these situations means that the driver is not in control of the car.
A plane is exactly the same. Turbulence does certainly exist which will cause the pilot to not be in perfect control of the plane, just as road conditions exist which will cause a driver to not be in control of their car. Like a car sliding off the road, you will really know if that happens! Your statement that the plane is "shaking uncontrollably" is simply not correct, any more than the normal road vibrations you get at 70mph indicate your car is "shaking uncontrollably". And if you're honest with yourself, you should recognise that the shaking you're experiencing is not anything different to what you feel on a daily basis in a car.
It's very simple, really. You are not frightened of turbulence. You are simply frightened of being in a situation where you are not in control of the vehicle you're in, and it really is as basic as that. In that situation, you have a natural nervousness about anything like the plane shaking - it isn't something you understand because you're not a pilot, and it isn't something you have any control over. You naturally feel uncomfortable owning a fear of not being in control, so you rationalise this to a fear of turbulence. But in reality the turbulence is just a symptomhook to hang a more basic fear on. I've seen adults have near-tantrums over having to queue for the toilets on a plane, and that equally clearly came down to them being uncomfortable in an unfamiliar environment which they can't control.
My top suggestion is perhaps paradoxical. Get a ride in a small plane or a microlight; maybe get a taster flight in a glider; or get a ride in a slightly larger plane like a Dakota or something at an airshow. In any of those you'll certainly feel a load of lumps and bumps from the air, because they're so much slower - but you'll be in direct sight of the pilot, perhaps within touching distance. You'll appreciate what kind of bumps can happen without the pilot being in the slightest bit out of control. Essentially inoculate yourself against your natural reaction with knowledge and experience. And then when you're in an airliner and there's a bit of a bump, you can think "ah, that's nothing, I know what's going on there".