How can I transform this circuit so that the output voltage not depending on the supply voltage of the amplifier(V2 and V1)?
Instead of feeding the amplifier output back to R2 and Runlabelled, put a resistor in series with the amplifier output, and a pair of back to back silicon diodes to ground, and connect R2 and Runlabelled to those. This will regulate the feedback voltage to roughly +/- 0.7, as long as V1 and V2 are sufficiently above that. Or use end to end Zeners, if 0.7v is too little.