Answer: I am pretty sure what you are seeing is the effect of water hammer. Water hammer (this also occurs with any fluid) is a pressure surge caused primarily by large changes in the volume of fluid being transported over a short period of time. Fugitive air that enters into water lines can also cause this.
Air can act as a buffer between two volumes of water. As the air escapes the system, the volumes of water before and after it slug the piping system when momentum is transferred. It is the impact or momentum of the water hitting the joints as it changes direction that is causing the swaying of your pipes. The secondary pipes branching off the main line probably do not have any impact resistance built into the connection to the main line and cannot handle the movement.
The most common problem that causes water hammer is either the trim design of the volume control valve used for this line or the speed at which the valve opens and closes. The slower the valve opens and closes, the more reduction you will see in the hammer. It is typical to have large buttress supports at major turns for piping this size. If not, this should be your next line of defense after adjusting the speed of your control valve.
If, because of system design, you need to have a control valve that opens and closes quickly, your problem just got raised to the next level of difficulty. The engineering calculations that are needed to design constraints, supports and pipe expansion joints are quite complex and very specific to a particular design. If this is the case, I would recommend either employing a design engineering firm to run the necessary calculations or going back to the firm that originally designed the system.