Bob,
o.k., it's not that simple as I made it look.
The beauty of a switch mode step down regulator is that the average current at the input is lower than at the output.
Assuming 80% efficiency, 5V*1A=5W -> 5W/0.8=6.25W at the input Since Vin=12V, this makes for I=6.25W/12V=0.52A.
To these 0.52A add 3A from the 12V leg and the average current is 3.52A. O.K., maybe going for a 4A supply puts you on the safe side.
I agree that the switched mode supply will draw pulsed current higher than the average 0.52A. Typically I'd expect Ipeak <=1A in this case. You can easily deliver this current from a good buffer capacitor. A rule of thumb is 1000µF per 1A, so placing at least 1000µF (again: to be on the safe side use 2200µF) low ESR capacitor between the 12V output and the step-down regulator's input will help. You can even place a series inductor from the 12V output to the capacitor and switch mode regulator to further filter and block the current spikes from the 12V rail - and to make the 12V supply see more an average current of 0.52A instead of the pulsed current.