While I'm not sure precisely what you're asking, I know you cannot have two pivots on a single object, but you can move the pivot point on an object by holding D while in the move tool or by hitting Insert (Or it might be End, i just tap around on my numpad until I see it go) and then dragging the pivot point.

If you want something to be movable from either side, like a bar on an axle that jostles up and down, then you need to do a simple joint chain- I would put the parent joint in the center of the bar, put one joint at either end of the bar, and then a fourth and fifth joint right at the movement points on the static objects. Mechanically bind the bar to the joint (with the parent function) and bind the fourth and fifth joints to the static objects. The second and third joints aren't bound to anything and act merely to make the other parts move correctly, unless there's separate spinning axles at the end, in which case you'll have a much more complex rig, and you'll have to figure it out yourself.

Here's a picture of a simple rig I did that I think will help: