How would I take this line and straighten it in illustrator without losing any of its length (Like if you held pulled a thread tight by both ends.)
You don't. Pulling or dragging something to straighten out a multi-curved path is not possible as far as I'm aware. You could move each and every anchor point, but then you'd be hard pressed to not alter the length of the curves as you moved points.
You can get the length and draw a new path.
Window > Document Info, then in the Document Info Panel Menu set it to
Objects and select your path. It will tell you the length of the path.
Draw a new path that length.
Have you tried resetting the Bezier curves using the pen tool? If you select and hold the pen tool from the sidebar 4 options should appear, select "anchor point tool" (shortcut for all of this is P > Shift + C) and simply click the anchor point. It'll remove the handles from that specific anchor point. When two points have no handles they become a straight line.