This would be better (output left open):
simulate this circuit – Schematic created using CircuitLab
Both inputs are within the common-mode range of the amplifer- see the datasheet which gives the values with a +/-6V supply and translate by adding 6V to the numbers.
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
What you need to do is add a couple of resistors
simulate this circuit – Schematic created using CircuitLab
If the instrumentation amp has a gain G, then, since the current through R1 must equal the current through R2,
Vin/R1 = G iL Rs/R2,
where iL is the load current.
Rearranging the terms gives
iL = Vin(R2 /R1 G Rs)
Note that, strictly speaking, an instrumentation amp is not required, since Rs is grounded, and a simple non-inverting op amp would do the job. In practice, an instrumentation amp would be a good idea, since tiny differences in ground resistance will have a noticeable effect due to the large gain of the amp.
Also note that this configuration will almost certainly oscillate like crazy. The phase shift caused by the instrumentation amp will need careful compensation.