1 - The cig lighter is NOT regulated 12v as you indicate.
2 - What is the relay circuit coming from the cig lighter used for? Your diagram indicates a circuit to nowhere.
3 - The fuses on the IGN line aren't necessary. They don't draw enough current to pose a danger. Granted, a fuse wouldn't hurt anything.
4 - A 120A fuse is probably overkill. I have a 100A fuse on 4AWG that powers a small inverter, the PC and two amps.