There are a few threads that get overlooked every now and then. I promise it has nothing to do with what you drive
So you have a CB that is rated to draw only 2 amps right,
The power cord you have has a 5 amp fuse in it,
The circuit you are using has a 20 amp fuse.
So what you need to do is change the fuse in the power cord to a 2 amp fuse so that it will protect your CB, and if your CB is drawing the full 2 amps you still can draw another 18 amps through the lighter circuit and it will not blow any fuses.
Just because you are drawing a heavy load on a circuit does not mean those amps are going to everything on that circuit so if you push in your lighter the current will flow through the 20 amp fuse to the cig lighter but it will not affect your CB other than perhaps reducing the amount of power that is available to it.
There are a lot of good people on this board that will help anyone with just about anything, its just that the electronics section is not real active. If what I wrote doesnt make sense let me know and I will try again
EDIT: Okay I read it myself and think I could do better
You are right if the only thing you have plugged in is the CB it SHOULD only draw 2 amps, now if something goes wrong with the CB and you leave that 5 amp fuse in there you run the risk of frying it, that is why you want to chang the fuse to a 2 amp, that way if something goes wrong you just blow a fuse, fix the problem, put a new fuse in and be on your way.