Electronic – Virtual ground circuit won’t work as expected

First off your Instrumentation Amp resistors should be high precision types, 1% or better. Without this your DRL circuit, as connected, is amplifying the gain error and DC offsets. (As a side note, the DRL circuit and connection do not quite look correct.) If this circuit must be used in this form with non-precision resistors consider changing one of the 1.8k parts to a 1.5k in series with a 500 ohm potentiometer, then tune to zero with shorted input signals.

Also, your input signals label V+ and V- are confusing while you discuss power supply voltages of V+ and V-, (obviously your input signals would be better named Left, Right, for biomed connections).

As other are hinting, the vref should be used to create the virtual ground with other input, see info below.

Lastly, for more specific info see the TI app sheet/report SBAA188-July 2011, on CM Rejection using Right=Leg-Drive Amp, at:
http://www.ti.com/lit/an/sbaa188/sbaa188.pdf

What if you use your second (or indeed first, or indeed any of all the other devices) with a device made by someone thinking the same as you with a shared supply in some larger encompassing device? Call the person and ask if the one ground is the same as the other ground? i.e. Is signal ground the same level as power ground?

I can tell you, in "cheap" designs many do it the same way as you, but often use the full power input to divide. So you are going to compete. Violently, if their reference is 12V/2.

If you want to make a good design that's universally compatible, you make sure that the external grounds are all actually the same hardwired level. So if you output a +5V and a 0V only, that 0V should be the same as the 0V on all the audio plugs. That's a good design.

So in this set-up, what would have been better is to output your original 5VDC as a +/- 2.5VDC balanced around your 'weak' virtual ground in a three pin plug. Then suddenly you have a balanced power supply to your second box and you could even devise a system where if the middle pin is not lifted to half VCC, then you make it yourself if needed. Or for separate use make a second DC plug with a switch built in that activates the divider and disconnects the 5VDC lines (for safety).

The high-end or 'common rail' design thing if you have a DC input jack, is to use a voltage inverter to obtain your negative rail, +9VDC --> -8VDC ; +9VDC --> +5VDC ; -8VDC --> -5VDC (or 2.5V for each, but then, use 5VDC in, for efficiency). Or even better a fully isolated balanced DC. Unfortunately nobody else who makes $10 gadgets does this, so you can't even assume it.

Want to use a divided VCC as a virtual ground with an external DC adapter and stay safe and compatible to "shared power situations"? One of two options:

1. You'll have to decouple and route the hard external ground through input and output or just force your own ground on the output again. It's not awesome, but it's what it is.
2. Add the DCDC isolation on the DC input I discussed before. If your consumption is as low as 1W DC/DC with +5V and 0V out or +3.3V, 0V and -3.3V out is about $5. Using the balanced with two low-drop 2.5V regulators, one negative one positive, will even get you much better thermal stability on the ground and its relation to your supplies. Plus, it sources and sinks the maximum available current with no problems or aberrations. In fact, doing that same trick with your original DC input would have been possible by first dividing the 9V to virtual ground and then dropping the original power lines to +2.5V and -2.5V.

If you go down the rabbit hole of "Oh, I'll just assume it's only a 0.1V difference", in six months you'll be kicking yourself, because you have a 9VDC system with a 4.5V virtual ground, etc.