1. 8awg is a good size to run, but you should run it the entire length. the total wire length is only as good as the smallest wire, the wire going to your dual outlets should be 8awg as well (use 8awg to connect to relay pins #30 and #87).
2. the relay coil wires (pins #86 and #85) do not carry much power. 1oawg is serious overkill for those wires (the ACC line you're going to connect it to is probably 20awg or smaller).
3. I wouldn't use cig lighter outlets. they don't make good connections (not much surface area for the positive connection, dirt builds up inside, and they can rattle/vibrate loose over time). it would be better to hardwire your power wires. if you want them to be easily removable, then you can use a set of male/female interlocking connectors.