Your choice of IC and LED parts looks fine. The 12V supply in a vehicle is a nasty environment to power a circuit from, so I would recommend adding an input filter and a regulator IC on the 12V. The best regulator would be a simple linear part that is designed specifically for automotive use but even the common 7808 would be a good choice. I suggest an 8 volt regulator simply because the 78xx series needs an input voltage that is 2 volts or so above the output voltage, and you can't count on the vehicle voltage remaining at 12V when the engine isn't running, so plan on an input of 10V. There are other linear regulators that are the "low drop out" type which only need an input that is about 0.5 volts above the output, but it seems your circuit could work just as well from 8 volts as it would from 10 or 12V. (when you crank your engine, the DC voltage will drop momentarily to as low as 4V and then go up to around 7 to 10V while the starter cranks. Don't expect your circuit to work properly during this time. Those of us designing microprocessor circuits for in vehicles should use a supervisor circuit to reset the processor during these brown-outs)
I would also recommend an input filter on the 12VDC input consisting of a a series fuse and a reversed shunt rectifier or power zener (30 volts). The rectifier would be bypassed by a 1000 pF 100 V ceramic cap. Then I would add a series common mode choke followed by a shunt capacitor, say 1 uF 50 voltDC. The fuse followed by the rectifier helps protect against accidental reverse hookup of the 12V DC, while the choke helps reduce alternator whine and other noise . But this may be overkill for your application.
The interconnect wiring that you add in your vehicle has the potential to act as an antenna and pick up your radio transmissions and bring RFI into your circuit. So you need to add some simple RF filtering to every wire that enters your circuit, in the form of a 470 pF (or any value from 100 to 1000 pF) 100VDC or higher, bypass capacitor to a good ground point in your new circuit. Put one of these ceramic capacitors from each speaker input to ground, and from 12Vinput to ground. Your ground should be the point where your ground wire from the vehicle attaches.
One other thing to watch for is that the circuit in the data sheet assumes that the speaker amplifier is single ended and not a bridge type. A bridge output has two speaker lines neither of which is ground, and you should not attach either side to ground. I don't think this is common in mobile radios. You need to check that. Post again if you don't know how to deal with this.