Help with Hyundai Sonata with chronic problems

We bought a used Hyundai Sonata about two years ago (then, it had about 56,000 miles). After about two months, the car started jerking a bit when I would accelerate to get onto the freeway. (I’ve debated with my mother-in-law whether to describe the phenomenon as a cough, jerk, catch, hiccup etc. Any of those could apply.) It was still under extended warranty for about a week (and the engine light had come on), so I took it to the dealer. Their mechanics told me that the engine light was a result of the gas cap not being on tight enough, and that some plastic piping needed replaced. They did this. I drove away and soon realized that nothing had changed, except that the light was now off.



I waited too long to get it fixed, the warranty ran out, and about a week later, as I was merging onto the freeway, the car “caught” again as I was accelerating, I heard a ping, the engine died and I quickly moved to the side of the road.



I was towed to a place the tow truck driver knew of, and we had a few parts replaced (including an oxygen sensor) and some exhaust parts. The thing worked again, but within a few weeks, it started having trouble accelerating again. We also noticed that the car would do its catching bit right when the car started, and if you didn’t gas it, it would occasionally stall.



For the last two years, we’ve periodically taken the car into the mechanic, he will run the diagnostic machine, fix whatever it calls for, and return the car. The problem never really goes away.



I just took the car in two months ago (prior to moving from Ohio to Washington, DC), but the car is really acting up now. I’ve noticed the following which may help with diagnostics: the car does its hiccupping (it really feels like it’s trying to switch gears, although it’s an automatic) around 2200 rpms (but also at other times–consistently though at this level), but also does it when you first start the car and even when the car first starts and it’s in reverse. It feels like the car is pulling to switch gears, but like it might just stall if it doesn’t manage to rev. Also, if you get up to 65 mph, pass over the 2200 rpms, (which gets the car to catch), then decelerate, it DOES NOT catch/cough/hiccup.

When the car first starts having this problem, it will catch just once, but as the problem progresses over months, it can consecutively catch up to 5-6 times.



It seems to be a more common phenomenon once the car is warmed up (if you drive, park, start the car again within half an hour and on the second drive it will happen), although occasionally, it will happen from cold. Some days are worse than others–really, I can find little rhyme or reason to what sets the car to acting finicky.



I’m scared that it will stop again on the freeway (and now I live right off the belt way!). I also don’t know any mechanics in my new area–and REALLY worry I’ll end up with someone else who only seems to know how to hook the car up to a diagnostic machine. Could there be a problem that a diagnostic machine wouldn’t be able to isolate???



I must also mention that I am NOT a car gal, so while advice is requested, please remember that I only have an elementary understanding of the workings of this machine.

Only thing I can add is start from the beginning,and the tech who gets this job must verify everything for himself. Dont accept previous conclusions