I've seen the wobbling with Dominators, though in my case it's the opposite shield situation: It wobbles under heavy fire with regular shields once it's fluxed out and has to take armor/hull hits. If I add Shield Shunt it will tank the incoming fire, remain steady, and fire back properly. Same basic loadout in both cases, with the main difference being hullmods.
Sometime I'll have to try removing some rear-facing weapons, although it has a full complement (big guns and PD) in the front and only PD in the sides/rear. Maybe it's trying to bring more PD to bear - it does have small mounts on the sides with a traverse that stops facing exactly parallel to the ship's facing, so wobbling a bit would give it the angle to hit missiles coming in from the front. Or, maybe AI indecisiveness about weapons and attempts to hide damaged hull can both cause this behavior.