Really Weird Issue

So I have a 2011 Aveo. Sometimes while driving (especially with a.c. on and a heavy electrical pull) all electronics including the engine and trans will shutoff for a split second. At interstate speeds it always comes back on immediately after a small jerk. If moving slowly I have to stop and turn the car back on. Additionally, sometimes when starting the car after sitting for any length of time, the car is 100% dead Or is functioning until I turn the key. When I turn the key either everything shuts off or all meters start shaking (lights flickering and needles moving up and down quickly.) I can open the main fuse box in the engine compartment and wiggle The ac compressor relay and the electronics will turn back on and off. Sometimes I can wiggle it just right and it's fine. Often times when I press the brake and the brake lights come on or if I turn the ac on it shuts everything down for a split second.

All that said it will go days functioning fine. I took it to the dealer and of course it wouldn't do it while it was there.... They said they can't troubleshoot it without duplicating. Lastly, I smell burning plastic in the fuse box and I saw a tiny puff of smoke twice when fiddling with it.

Probably bad relay or box? Where should I start?

oh that's bad. I would do something now before you get yourself killed. Like it shuts down on a railroad track or something (yes it's melodramatic).

I pulled my fuse box apart and it's wires to pins. I think the later ones was wires to a circuit board. So I would start there and make sure nothing is shorting. Relay box and fuse box in engine compartment one and the same.