Grounded/Earthed electric circuits

The ground connection has no bearing on combining capacitors C2 and C3 in parallel. It is simply a point where zero potential is typically assigned.

I combine the two capacitors. If the battery supplies 12 V and C1 is 8uF I have calculated that the charge on C1 is 96uC. How does the current then split between the newly combined capacitor and the voltmeter?

Assuming the circuit shown has existed for a long time so that transients, if any, have died out, then there is no current flowing anywhere in the circuit. In order for current to flow the voltages have to be changing in time.

That being said, you can calculate how the battery voltage splits between C1 and the parallel combination of C2/C3.

First of all, the charge on C1 is not 96uC because all of the battery voltage is not across C1. You need to determine the equivalent capacitance across the battery by combining all three capacitors to get the equivalent capacitance $C_{eq}$. Then the total charge on the equivalent capacitance is $12C_{eq}$.

Next put back all the capacitors. The total charge will be equally split between C1 and the parallel combination of C2/C3 because they are series capacitors and all capacitors in series have to have the same charge.

Finally, you can calculate the voltage across C1 and the C2/C3. The voltage across C2/C3 is that read by the voltmeter.

Hope this helps.