Method 1) Connect the 120 volt neutral to the circuit ground, then use T1 to send current through a resistor to the gate of a triac and connect one end of the nichrome to the 120 circuit and the other end to the anode of the triac. The third terminal of the triac goes to ground. The collector of T1 goes to the +12 supply.
method 2) Don't connect the 120 neutral to the circuit ground. Have T1 drive an opto-isolator and have that drives a triac. The nichrome power circuit will stand seperate from your primary circuitry, connected only by a light beam inside the opto-isolator.
method 3) Use the relay to send +12 to a resistor, to a triac as in method 1
method 4) Use the relay to send +12 to an opto-isolator to drive a triac as in method 2.
No matter which method, you must use a small inductor in series with the nichrome to keep the inrush current from frying the triac.