Does this seem right?
It looks pretty good to me. Make sure that you have considered all possibilities. To ensure that you have, find a 10 year old, and have them start the car, using only the instructions that you have written down. If the 10 year old can start the car, without damaging anything, then the Arduino should have no problems starting it.
Test each part of the code separately, before trying to combine all the code into one program.
For instance, make sure that you can detect each switch, and that the alternator is read correctly, after starting the car manually. Make sure that the relays open and close when they are supposed to, with nothing connected to them. Make sure that they still open and close correctly with a load on them.