Ok so I've got an Adafruit 4 channel motor shield driving a 150mA 12v DC Brushless motor, a 120mA fan and a 1.2A 9V DC water pump at alternating times. I'm using a 12V external power supply with a 1.5A current rating to power the motor shield. Issue is all the motors function properly accept when its time to turn the pump on. The pump initializes with strong voltage to begin with but then drops off almost instantly. I'm thinking of using a Relay module off my channel 2 driver off the shield. I do understand the principles of how relays works except one thing. The question is can i use this channel to switch the relay on with another 9v power supply dedicated to the pump through the relay. And if I can, do I just hook the INT terminal from the relay module input to the positive channel 2 on the motor shield to receive the high to low or low to high switch?

If the 1.5 amp power supply is powering the 1.2A pump as well as the the other things my guess is that it cannot provide enough amps. The pump will probably draw a lot more than 1.2A at startup. Your power supply needs to be able to provide the stall current for the pump with a comfortable margin.

If I have misunderstood things please provide a diagram showing how everything is connected. A photo of a clear pencil drawing will be fine.