Thank you. After some thought, a diagram of my circuit is here. (At least the portion that handles powering the Arduino according to the state of doors and locks.)
None of the 5 relays is latching, although one of the relays (labeled "Power Hold") is used to latch the power supply. Three relays must be DPDT (12v), one can be SPDT (12v) (or wired as such), and the last one can also be SPDT (5v).
For simplicity, my original post didn't mention:
1) The Arduino would be powered up upon any of three conditions: A door is locked/unlocked, A door opens, or the key is turned.
2) The Arduino has a real-time clock, so even if it loses power and comes back on, it knows how long ago any of the above conditions were last met.
3) The whole purpose is to control video and audio recording onboard a fleet of vehicles, which I own for a my driving school business. It will record for a set time after the car is left unattended, and in addition to the circuitry shown, there is a pushbutton and display on the dash which allows the driver to disable video recording for a specified time period.... (Therefore there will be a 6th relay and related transistor, not shown, which affects 12V power to the mobile DVR.) This is for driving instructors, my employees, who normally need to be recorded. But since students can legally deny consent to be recorded, they need to be able to disable it for the length of one lesson, no more than twice per day. It must default to record, but if disabled it should resume recording after a timeout.
4) In an earlier implementation, the system froze occasionally in real life use. (Either the display or the Arduino.) I don't know why. (Heat, memory management, etc.) I can't know for sure it won't happen again, and therefore, this implementation resets the Arduino by momentarily removing power while the key fob "lock" or "unlock" buttons are pressed. This doesn't disrupt anything because upon startup, the Arduino remembers what it was last doing, and checks it realtime clock against the time that it was supposed to resume or stop recording.
My original question remains, although slightly different: Although I won't use a latching type relay, are the relays shown in the spec sheet of my original post appropriate? (The spec sheet includes 5V and 12V relays, DPDT, and not all of them latch.)
EDIT, Minor correction: There's no reason they can't all be 12V DPDT relays, even if I don't use the second switch. So consider my diagram modified to use 12V for the rightmost relay. My concern is what jremmington said above: "The car cannot safely provide the voltage required for the relay, so you will need extra circuitry." Respectfully, that doesn't sound correct to me. I know the car voltage is noisy and unstable, but to my knowledge a relay coil isn't sensitive like a mircocontroller, and the Arduino itself is getting clean, regulated 9V power.