Virtual ground concept in electronic circuit
The &quot;0V reference&quot; is created by the TLE2426D:

So, initially, to match only your simulation, the power rails would become:

The 0V connection to the input (if needed) can't be determined without knowing more about that you are measuring.
But, according to your text I assume you are powering your arduino from the 12V (which is correct) and not from the TLE2426, and you want your output varying from 0 to 5V according to the power supply. From a previous post, I also assume you need to measure V4 with both polarities. Hence, the INA output, according to the 12 V power supply and your gain and ref:
$$V_4=-50mV \rightarrow  V_{INA} \approx 2.25 V$$
$$V_4=50mV \rightarrow  V_{INA} \approx 7.25 V$$
Is this correct? If it is, you need to &quot;shift down&quot; the output by 2.25V, and not multiply it by two. You could provide this shift by applying a different reference to the INA, using the op. amp. as a voltage follower connected to a voltage divider.