The swamp cooler needs a breaker on whatever curcuit it's on. If you pull 120 volts off of one leg of the 240 volts, the breaker for that leg is actually only on one pole of the 240 dipole that runs your A/C unit. You will be pulling an uneven load off of the A/C line.
Also, im a little confused on the set up. For your A/C, there should be a black, red, and ground coming from the panel if its 8/2, or black, red, white, and green if it's 8/3 (i'm assuming #8 since the A/C unit is most likely on a 40 amp dipole.
You need to call a qualified eletrician to fix your problem