Turns out your clans can still get into feuds when they are sent to Rome for either training or for the Magister Militum quest. If they're in training you can still access them to punish them (they count as being in your settlement, which is the problem, actually) but when they're off conquering Rome they seem to be totally inaccessible, meaning you have to either just live with it or punish the (probably high-level) clan back home. This seems less than ideal!