Isn't this assuming that there are several actual laws and codes lain down? As I recall duelling 101 on a simple basis, the one who challenges doesn't get to pick weapons and such.
Besides, as Jon states, she isn't a "real" duchess, so it actually is beneath the Baron's status and thus she is the one insulting *him*, speaking up against a higher ranked noble (giving him ample reason to call upon "his" champion).
Oh now that opens a can of worms - who has the 'right to the title' - a common cause of duels. If you can ignore a 'title' just because you feel that it is yours and not theirs then the entire system falls down - the incumbent may be 'proven' not to hold right to the title in duel, but untilthey lose the duel they hold it - and no sane system will suggest differently.
The insult by the way is not her claiming title, or usurping his rank - that happened far too long ago - again duelling codes will vary, but most demand that the insult is recent. Not difficult to circumvent if you want a duel - you just blow off about it and then the insult is new again - but the question of 'who first through the insult' at the S&C if judged is very likely to be the Baron... as for which set of rules let you pick time/place, weapons etc that will vary, but usually it will be 'the victim' simply because that protects against the killer-picking-fights scenario.
As for substitution, substitutes were quite rare - particularly if the party was healthy. Can a duke have their leg-breakers beat up a commoner? yes - but that isn't a duel its the law. Can two nobles insult each other and then one hide behind a professional killer? Not a chance in hell, the whole point is that they are the ones offended, and that as nobles there honour is their life.
And then you comes to scions - bloodtheft is heresy, outlawed - think of why. Why would the churches outlaw scions hunting each other down and going highlander? Answer it would lead to the extermination of the upper class as a gorgon-style killer simply walked around picking dues, claiming the others bloodline and go on to kill again.
The GN may want to draw drago into a duel, but he should damn well have the guts to go into the cathederal and challenge him directly - picking a fight with the man's sister frankly shames him. He may want to kill a mage for fun, fine, but he has to personally challenge her to do so.
And certainly if the GN simply kills the SM after disarming her, instead of offering her the chance to apologise, is waay out of line - the SM should of course call for pause and apologise (bit your tongue woman! you lost, that's the rules!) - but any chivalrous opponent will remind a defeated duellist of the option rather than gloating over their victory and going for the kill....
As for 'why have any rules' the present fiasco is the obvious reason - seconds arrange everything so that all agree that it is 'fair' or 'legal' - and so that loopy lovers and honour-bound fools don't charge in if their man is losing.