Is it possible to order a unit to point A ( owned by you ) and have it go to Point A without you being able to stop it from going to Point A?
A big factor is there are units going back and forth from Point A to Point B, and Point B to Point A, all at the same time.

Only through repeated ordering of the unit, so that any orders the player gives it will be overrided quickly, or by giving the unit to another player to prevent the human from ordering it differently. If you give the unit to P9-11, it will retain it's original player colour, then you could give it back at the destination.

They would have to remain your unit the whole time, I forgot to say there are six players that this is happening to, and they can walk in-between each other. It would also have to be the same unit.

Are you able to use the hero of each units that are going to be used? if so, I would suggest using it so you don't need any advance triggering that could possibly mess up if not done properly.

If you can't use heroes, maybe you could just move the units back from location A to location B so that the units would only go one way.

Make a parallel path so that units going one way will not be mixed with units going the other way.

Detect (Using EUD) if a unit of that kind was selected and make a trigger that will give all units to player 9 and back. (There may be a 2 second delay so...)

If you want to use EUD actions, you can always make you units un-selectable (You would have to find the right address if it was not already found.).

The possibilities are limited to your map idea so if you can't make starcraft fit into it, adapt your map to starcraft's limitations, sometimes just a little change will do the same result and will not change the whole game-play.

Hope that helped.

If there's more than 1 unit per player then things get difficult. You will have to follow each of the units with a 1x1 pixel location and keep track of which units are walking up and which are walking back down.
In any case you will need hyper triggers.

If there's many units (more than you can follow by 1x1 pixel locations) you could use Apos' method: Make them take slightly different paths like the left and the right side of a road. Elaboration:
You could have rail shaped locations (if exactly vertical or horizontal paths) to save locations. Problems could possibly arise when the units take detours because of obstacles (e.g. slower units) or are not sent straight along the line, which the SC path finding AI loves to do. Widen the rails as much as possible to prevent units from leaving them.
If that doesn't help you could add buffer locations along the rails that get the units back on track but that triples the location cost and the units might go backwards for a bit sometimes. And locations are a valuable resource in SC mapping.

Apos's method sounds like it would work for what I need ( I believe ). Any hero units would go to Point B, any non-hero would go to point A. It will work perfectly as long as I have both available units. Therefore, I could spam the order unit command.