I don't ride amusement park rides for exactly that reason. The motion and speed and such don't bother me, and it's not that I get dizzy or nauseous or anything. It's that I'm hyper-aware of the fact that all it would take to kill me is for one little mechanical part to fail or be incorrectly installed.
I actually fixate on specific parts - the whole time the ride's going, I'm looking around and thinking, "If that pin shears, I'm dead. If that bolt wasn't tightened down, I'm dead. If that flange twists, I'm dead."
I can manage cars, but I have a sort of mental block I've had to adopt to stop myself thinking about tires blowing out. It helps that I can't see them.
I generally only ride elevators if it's more floors than I can comfortably climb stairs, and I don't like them. Given the opportunity, I always take the stairs. And I spend a lot of my time on elevators specifically trying not to think about the arrangement of pulleys and cables that's the only thing standing between me and death. Again though, it helps that I can't actually see them.
Airplanes are sort of odd, because they don't much scare me. I think the whole thing is so complex and foreign that I can't get a firm idea of what specifically could fail, so I don't have any specific thing on which to focus the fear. I dunno - I just know that they don't scare me.
Trains are a bit unsettling though, I guess because wheels and rails are something on which I can and thus do focus. It's va fairly distant rhing though, and thinking about it is the exception rather than the rule.
With how elevators are engineered these days, it would be difficult to cause one to fall even deliberately. Multiple simultaneous system failures would be required that aren't fragile to begin with. Not sure about the particulars of your anxiety, but that one you might find some relief from through research.
You can also see tests of them, which gets performed on each and everyone before certification, where they are loaded to their max weight and are allowed to slam into the buffers at the bottom. It would be uncomfortable, but survivable.
Even if you were to ride an amusement park rollercoaster every single day for the rest of your life, you would be a couple magnitudes more likely to die on the car ride to or back from the park than by a malfunction of the attraction. Most malfunctions will result on the car stopping on an horizontal section then getting evacuated on foot, and that would be scary but you wouldn't be in any danger. You are in greater danger of harm or death stepping into a bathtub for a shower than on a rollercoaster cart riding at 120 km/h and pulling some Gs. Humans suck at intuitively assessing risk.