OK. First, delete the water hoses from your electrical diagram, it's confusing.

Second: get a wiring diagram for the vehicle. Think of it as a road map and you'll be able to read it fine with a bit of effort. An hour searching the net on how to read a chematic will do wonders for you.

Every vehicle has a distribution junction where the positive cable branches out to feed the various circuits. Ultimately, that is where the alternator output and sense wires must go. The way it is wired now, the alternator can only sense the voltage at the battery. It will cause reduced voltage to everything.

Think of the relay as a coil and a switch. Two contacts feed the coil, and the others the switch. One side of the coil goes to ground. The other gets positive from a control. In your case, I'm guessing a toggle switch. When the coil is energized it closes the switch.

Depending on the relay, it could have more than one switch, and the switch could have normally open and normally closed contacts. If it has both N.O. and N.C. then it will have three contacts per switch. One will be common, one N.C. and the third will be N.O. for what you are doing the source voltage should go to the common, and the load goes to the N.O.

Your wire is burning up : 12 AWG is more than heavy enough for a choke (16 AWG should be ok) so you have an additional issue there somewhere. Crappy terminals or poor crimping maybe. I'm guessing the choke is wired to the N.C. relay contact, so that it is on when the relay is off and vise versa.

If I'm interpreting your diagram correctly, you are trying to use the alternator output to control or "fire" the relay. Bad idea. Wire the relay to the stock ignition or a toggle switch.