Its a few years since I "flew" a 737-200 simulator which was the Lan Chile machine in Santiago, Chile. The visuals were poor and I had doubts about its fidelity. I know for the 737-300 simulator you need to keep in mind that the take off stabiliser trim setting is based upon a two engine VR. Obviously same with the 737-200.
If an engine fails while you are still between V1 and VR, be prepared for a heavy pull at VR much more than you would normally expect. That is because with one engine failed on the runway, the vertical vector of thrust normal with both engines going, is halved. That translates into a nose heavy pull off the ground. Best thing is to ask the simulator instructor to hop in a seat and demonstrate the manoeuvre - if he is game to. Most won't because they are not confident to demo an engine failure on take off without making a fool of themselves
In the simulator with engine failure at V1, we frequently see people relaxing on the heavy back pressure during rotation and flying back into the runway a couple of skips before getting airborne. So be prepared for real muscling to get the aircraft up near to 10-13 degrees. When well clear of the ground by about 200 feet then a fair amount of back stab trim (about three seconds) is needed to unload the back pressure.