A instrumentation amplifier is more than just a opamp hooked up as a differential amplifier. The inamp puts buffers in front of each of the diff amp inputs. This presents a high impedance to the outside, and also eliminates the cross impedance between the inputs of a bare diff amp.
In theory you could make a inamp with three opamps, but in practise that still won't be as good. A real inamp benefits from all the components being on a single die, which help in matching thermal characteristics and ballancing the gain of each input to get better common mode rejection. Precision inamps go thru a laser trimming process in production to get the absolute and relative gains just right.
You have wildly complicated your circuit, assuming your symbols mean what the schematic indicates.
First, an instrumentation amp would look like
simulate this circuit – Schematic created using CircuitLab
You show the upper amplifier, which produces OutInv, as being connected to the same ground as R3 and R9. Under these circumstances, OutInv is forced to ground (plus the input offset of the op amp), so you could profitably get rid of the op amp. Furthermore, a gain of 100 is perfectly reasonable from a single op amp, so you could do the whole thing with 1 op amp, as George Herold suggested. A simple version would be
simulate this circuit
This will have a nominal gain of 101. Since an LM358 has a maximum offset voltage of 7 mV, you could have an offset error of 0.7 volts.
Let's assume, though, that the two input grounds are instead a separate ground, isolated from the output ground by some common-mode voltage. In this case, you have connected the upper op amp incorrectly. R1 should be connected to the - input of both amps. However, if you do this, you'll have gain of about 220, rather than 100. The equation for gain for an instrumentation amplifier (assuming R2 equals R3, R4 equals R5, and R6 = R7) is$$G=(1+\frac{2R_2}{R_1})\frac{R_6}{R_5}$$ Alternatively, depending on the output impedance of V1, you could simply use a single op amp set up as a difference amplifier with a gain of 100. You've shown the V1 as a voltage source, so this seems perfectly reasonable.
If you're worried about a stable output, I assume you're worried about noise from the input. This is best handled with an RC filter between V1 and the input.
Best Answer
You need a ground between the two input voltage sources as @Neil says and you also need to ground the point between the two 12V sources.
The models used in this simulation must have some hidden 10G or whatever resistors because SPICE will fail to find a solution without a ground reference.