The 12V on your vehicle will probably drop below 12V while you start the engine. That, and the noise/spikes on top of the 12V means a simple linear regulator like the one you have in your diagram won't do what you want or expect.
Your circuit is for an input of 12.8V to 30V and it produces an output which is 12V and a little less noisy. If the input voltage (specified at 12.8V) fell a few hundred milli-volts the output would do the same and probably more so, for a 12V input you might only be getting 11V out and, the circuit is no longer regulating. It is providing some input noise rejection but probably not enough as you might expect.
The next question is how low can you tolerate the supply to fall below 12V before the pico motherboard, 7" lcd monitor and and arduino don't work. If it's 10V then you might be OK but not during the period when you start the engine because the input voltage could drop to below 8V - then you'll only be getting about 6 or 7 volts from the circuit.
Ideally, and without fully understanding what you really need I'd go for a buck boost regulator and there are plenty to choose from Linear Technology amongst others.: -
