PROBLEM: You want to know if there is a quicker way to remove multpile vertices between two selected vertices instead of using the PE command and straighten.
RESOLUTION: In command line type WEEDFEATURES, then P for Partial. Select the start and end points for where you want to weed. Set settings to just length and a large value and the line will straighten.
Note that this is a bit trickier if the start and end points of your polyline are within the section being straightened, as you have to do it in two steps up to that point then remove manually.
Another option is to just break the polyline at two points, delete the unwanted piece, then add a new one.