I'm sorry if my problem was not clear previously I am looking to use the data received by the IR remote (which I understand) to cause the steppers to operate simultaneously for a large number of steps when a signal is received, but I don't know which Accelstepper function to use in order to make this happen instead of the run function.
You need to understand when and why to call run(), and what it does if you call it when it is not needed.
Here's a hint: run() does NOTHING if the stepper is at the last commanded position.
So, on EVERY pass through loop(), call run() for each stepper.
When you press a button on the remote, you MIGHT want to change the position where the stepper is trying to get to.