The idea has proven to be good.
Now, any time a vehicle moves (by player or by environment, etc.) the event of that movement is sent to the rest of the players. Those other clients receive a message, read where that vehicle must be, and let the robot handle the operation of the vehicle to achieve the desired position and rotation.
According to my tests, it definitely overcomes lag. The worst case scenario is when an event comes in rather late (lag). The vehicle does lag behind the actual location on the originating client, but the robot does move the vehicle to the desired location and rotation. So, this works great.
I have also implemented accuracy setting. Movement updates are sent every time current position is P units far away from the last sent position, or the rotation is R degrees different from the last rotation sent. Currently, this pair of values (P,R) is (1,5), where P=1 means 1/6 of the vehicle's length.
These values have direct affect on two things. One is the accuracy of replication across the network. Another is how much trouble the robot has to go through to achieve the desired position and rotation.
This last issue can be a problem at low values of P and R. The reason is that vehicle does not turn on a dime, instead its turning mechanism (4 wheels on one side, 4 more on another side) has an error, so the rotation causes the tank to move away from its original position. This means that vehicle gets too far from the desired position (more than P units), and now it must first get back into the position, before continuing to turn. You can now imagine that at low values, this turning error will cause the robot to really struggle to get the vehicle into the position. And that is what it did in my tests.
While the above is not a problem, since I intend to keep values of P and R high, it is an indication that turning mechanism of the tank must be improved. One possible solution is to alter the power of both sides (set of 4 wheels) in order to achieve equal turning power, kind of like ABS for vehicles, which alters the power of the breaks on the wheels to prevent loss of contact with the ground. This is, however, is rather complex, so if I do decide to do it, it won't be soon.