Car bucking and acceleration problem?

The car listed above is an SXT model. My stepson borrowed it and while driving it shut off.
My husband tried to jumpstart many times and ended up with a new battery. The new battery installed still would not start.
Brought to a mechanic and he changed my serpentine belt, timing belt kit, crank sensor, cam sensor, gave me an oil change and changed filter. Drive good on way home except all dash lights were on. I went to work the next day and got on I95. Soon as I took off the entire car bucked as if my traction control activated and it did this at least 30 times in a 5 miles radius. I got off exit and came home back roads to go slower and it still did it. I was told to change my computer system and have programmed, which I did. Same thing, then the front and rear wheel abs wheel sensors. Still not fixed. Finally, I was told to have my ABS control module changed and drive a 100 miles. After 30 miles it is again not fixed. The car hesitates when you step on the gas and takes forever to gain speed, once I do, I get the bucking. The only difference is now the only light off is the abs light and anti-lock.