Hi,
Your input is not 200mV, it's 400mV. You have 200mV on Vip and -200mV on Vin. Since this is a differential input Vip-Vin is 400mV.
If the load is the OTA to be tested connected in unity gain feedback path (this means the load acts as a resistor of value 1/gm), the the output voltage will be: Vo=gm*Vin/gm=Vin. So the first circuit doesn't need a feedback path.
Sorry, I did a mistake. I thought that the 200mV comes from the Vsin sources, but it comes from the DC source.
We can't tell what's wrong in this case, unless you show us how the OTA schematic.