How does current split in this circuit?
There is 54 V across the capacitor at steady state with the switch open:


plus side of the capacitor is at +50 V   ....    0.01 mA * 5 KOhm
negative side of capacitor is at -4 V     ....   -6 V * 2/3


There is only transient current that flow through the capacitor and the current source and voltage source are completely separate.   

When the switch closes then instantaneously there will be -54 V at the junction of the 2k and 4k resistor. Current will flow from the 6 V supply to satisfy the time constant of the RC values as the capacitor discharges to 0 V.