I haven't specifically tested what you are talking about, but I never found that FAM worked differently in coop than in ladder/global games.
If you hold shift to drag a factory attack-move order, you will change that order for all units/buildings that share that order. It doesn't matter which unit is selected. Clicking on the engineer to select it is irrelevant. The fact that you are talking about clicking on the engineer, I think shows where your mistake is. Any time you use "shift" and drag an order, it doesn't matter what units (if any) are selected.
If you want to be able to move the factory attack-move order for 1 engineer, but keep it the same for the factory, what you need to do is click on the factory, and give it new orders (a new attack-move order). Then, you can move the preexisting attack-move order, and you will be changing orders for the existing engineers, but not for the factory itself. In general, if you want to make a factory that spams out factory attack-move engineers, it's good to click on the factory and give it a new/different attack-move order basically every time an engineer comes out. That way you can use shift to drag multiple attack-move orders and each one will belong to a single engineer, so you can most-efficiently spread out your reclaimers.
The key to understanding attack move is as follows. There are two kinds of attack move, "normal attack-move" (NAM) and "factory attack-move" (FAM).
Units on NAM behave just like they are on patrol. They will travel towards the waypoint, but while they're traveling, they will get distracted by stuff they can do, like reclaiming trees. An engineer on NAM can travel across the map, reclaiming rocks along the way. When it gets to the waypoint it will continue to do engineer stuff (reclaiming rocks within a certain range, including traveling from the waypoint to a nearby spot in order to reclaim a rock that was outside of its build range). When it's at the waypoint and it runs out of engineer stuff to do (nothing else to reclaim, or it can't reclaim rocks because your mass bar is full) the order is removed from this unit's queue and it moves on to the next order (if there is a next order, otherwise it becomes idle).
Units on FAM behave very differently: they travel directly to the waypoint without stopping. Then they do engineer stuff (reclaiming rocks/trees within their "guard" range) until they run out of engineer stuff to do. They can reclaim stuff that is much farther away than under any other circumstance. They can reclaim stuff within their "guard" range instead of only being able to reclaim stuff within their "build" range. So unlike an engineer on NAM, a FAM engineer does not have to move in order to reclaim the same stuff, which is why FAM engineers are more efficient at reclaiming. When it runs out of engineer things to do within its guard range, the FAM order ends and the engineer becomes idle. (a FAM engineer never has another order after the FAM order)
So that's the difference in how they behave, which explains why you would prefer to have a FAM engineer (basically the only reason is that they can reclaim stuff a lot faster).
FAM is an engine bug. In theory, the FAF team could considered it to be an exploit, and ban it, but that would be hard to enforce and players wouldn't like it. So it's just considered to be part of the game and you're allowed/encouraged to "abuse" it as much as you can.
Here's how you get FAM to happen:
You can't give a FAM order to an existing engineer that has already been built. Any order that you give to an existing engineer will always be NAM. Even if you tell the engineer to "assist" another engineer on FAM, the assisting engineer will not behave like FAM.
The only way to make a FAM order is for the factory to assign the engineer to "attack-move." This attack-move order must be the last order from the factory (when the engineer comes out--after the engineer comes out, you can change the factory's orders without affecting any already-built engineers). The attack-move order must not be preceded by any other attack-move orders but it can have any number of move orders before it.
So you can get FAM with a factory that has only 1 order for units coming out, a single attack-move order. Or you can give 1+ move orders before a single attack-move order. In those circumstances, engineers coming out will do FAM. You can't get FAM if your factory has 2 attack-moves in the queue. You can't get FAM if you have an attack-move order followed by a move order. If you do that, the engineers that come out will act like every attack-move order is a regular attack move. I haven't tested it in a while, but I think you can put in a "ferry" order in the queue before the final attack-move order, and the final order will still be a FAM.
FAM tends to be most effective when only 1 engineer is acting according to the FAM order. It is more efficient to have 4 engineers to come out of a factory, each with their own unique FAM order (so 4 total) than to have 4 engineers sharing a single FAM order. This is because 4 engineers can reclaim faster if you spread them out compared to if they all have to move to the same point. You can accomplish this by selecting the factory every time an engineer comes out, and giving it new orders (a new attack-move order) so that the existing engineer keeps the preexisting order and new engineers will get the new order.