ok, so there is no user switch, just PC_USB power as signal to switch... the way i read it..
1) SWITCH_ON_SIGNAL will always 0V regardless of PC_USB level so R1, C1, Q1, R3, R12, Q4, R13 is useless. in fact if you install Q4, it will render SWITCH_SIGNAL useless, see below.
2) what makes the difference is SWITCH_SIGNAL will be pulled low whenever PC_USB is turn on. otherwise turning on relay by U3A (open collector comparator i guess) if there AMP_SIGNAL_ON is HI. but if you install Q4, it will pull the SWITCH_SIGNAL low again.
3) U2A, R2, C2 is not doing anything except wasting current, so they are useless as well. IF U2A is not open collector
4) if they are open collector, U2A and U3A will form AND circuit to RELAY_SIGNAL. you can do that with few transistors. google that in wiki.