Transmission problem

About a month I was having very rough shifting with each change of gear (reverse, drive, etc.) I took it to the dealership and they tried to reprogram the computer. That seemed to solve the problem. About a week and a half later I went into a store and came back to my car. Upon turning the car on and putting it in reverse I had the same sort of "jerk" that I had experienced before but only in reverse. I took it back to the dealer and they said I need a new transmission which costs between $2,800.00 to $2,900.00. I took it to a local mechanic for a second opinion. He saw no codes. Not sure if the dealer cleared the codes. He drove it a bit and noticed engine problems but not transmission problems. I do not understand what he did but I fully trust this guy. $650.00 later the problem is not fixed. He did not say that fixing the engine problem would fix the shifting issue but he said it might. Well, now it sometimes shifts hard in reverse but only when the car if hot (after being driven five miles or so and only after it is turned off and then back on. For example I went to a gas station, turned the car off tried reverse and it "jumped" again. But it only happens sometimes. Took it back to the mechanic. No codes. He drove it over the weekend saw nothing wrong with it. Said something like the air cycles and it may feel harder shifting into reverse (but honestly I do not really understand what he said or what he was talking about.) So I asked him to try it out for one more day and see if he can detect anything. I will find out tomorrow but I doubt it if he could not find anything over the weekend. I have a rental. It is a new Elantra and I have not felt anything on any shifts so I do not understand. I know this is long but does anyone have any opinion or guess on what might be going on? Thank you in advance!