Sputtering, stalling

Have you read the diagnostic fault codes? Do you have the single or dual cam engine?

Based on the mileage, consider checking the timing belt and timing.

When there are no fault codes, you need to connect a scanner to look at the data the engine computer sees and is responding to. You will need to know what "normal" is so you can identify what is not right. Also, most scanners have a record feature. This will help in cases like this when a problem only acts up at certain times, like when accelerating, and you cannot be distract by reading the display. You press the "record" button when the sputtering occurs, then it will record a few seconds of data that you can play back slowly, later, and watch what changes. Since the data passes through the scanner's memory, the recording actually starts a few seconds before you pressed the button.

Does the radiator fan run at times? If it is not working, the engine will not overheat when driving at highway speeds because of natural air flow.

You can check the operation of the fan system by turning on the ignition switch, then unplugging the two-wire coolant temperature sensor. That will make the engine computer turn on the fan relay, and the fan should run.