Differential Pair with non-differential inputs
But I'm wondering, what would happen if Vin1 went up by 10mV, but Vin2 stayed the same and didn't go down by 10mV. 


You need to work out the common mode and differential components of the input.

For example, your scenario is the same as both inputs going up by 5 mV, then Vin1 going up by another 5 mV while Vin2 goes down by 5 mV.

Roughly, the output would be the same as if you just had a 10 mV differential input. But if the amplifier is not well balanced you could also see an output change due to the 5 mV common mode input.