Setting the dial to M only affects the camera's exposure mode but does not tell the camera to also use manual flash mode any more than it tells the camera to use manual focusing mode. There are a couple of other options you need to check that could be causing the camera to emit the pre-flash.

• Red-eye reduction. The camera fires a pre-flash to try and induce the subject's pupils to contract so less light from the main flash is allowed to enter the eye, bounce off the back of the inside of the eye and back out through the iris. Instructions for enabling or disabling red-eye reduction are found on page 65 of the T2i Instruction Manual.
• E-TTL. Since you are optically triggering another flash without an E-TTL capable master flash, in the Canon system this means you are not using E-TTL to communicate with the off camera flash. But your camera has no idea the off camera flash even exists, since it is not in communication with it. If the flash mode on the camera is set to E-TTL then the camera is assuming the built-in flash is the only one and is going to fire a pre-flash to meter the reflectivity of the subject. Unfortunately, page 148 of the T2i Instruction Manual indicates that E-TTL is the only option with the built-in flash. To select Manual flash you must have a compatible external Speedlight attached to the T2i.

Since the T2i does not include a PC port (so you could disable the built-in flash and use the PC port to trigger the external flash via either a wired or wireless connection) the most practical workaround would probably be to use a cheap wireless trigger set (or the version with two receivers so you could use two off-camera flashes). By attaching the trigger's transmitter to the hot shoe, the camera should default to manual flash mode since it will not sense it as an E-TTL compatible flash. You may have to disable the built-in flash via the instructions on page 147 of the T2i Instruction Manual to prevent it from popping up. This may or may not prevent the hot shoe from signalling the transmitter when the shutter has opened.

Note that even though the flash sync speed of the T2i is 1/200 second, when using an off-camera flash via a wireless trigger you may have to reduce the shutter speed to slightly longer than the X-sync speed to insure the flash fires before the second curtain begins to close. If you see a dark rectangular area across the bottom of the picture, reduce the shutter speed to 1/160, 1/125, or even 1/100 second.