ummmm....even if you had it wired properly I doubt very seriously that a .5 Amp relay will work for you. You are gonna need a bigger one....you mentioned this one was from Radio Shack....well you can get a 30Amp Auto relay there for like $5.....
Also I am hoping that you have a fuse between the car battery and the relay.
Your setup is pretty much exactly like mine...and I have issues even with my 30Amp relay....I have burnt out 3 in the last couple of months
also do you have a diode in place?
Actaully now that I look at you setup I am confused as to why you want a relay attached to the inverter switch.....I believe what you want is to have the inverter turn on with the ignition?
If so you want to leave the inverter switch alone and wire the relay to the pole that powers the inverter. and the switched power would come from a AMP or your HU or something.....I will post a pic if you need a illustration.