The main point is that, while long term it might be desirable, we should expect a near immediate escalation to the war to either silence the defectors or else secure their own counterbalance advantage in order to ensure that nobody is in a position to just win against them.
As in within the week.
Doubt it.
There's a couple of factors that say otherwise IMO.
1)They dont have the intelligence.
While they can be certain that Arianna is dead(the Red King will know about his daughter, if nothing else) they dont know about the rest. They dont know if there are any survivors, if and where they were moved, or how to get there, or what the opposition is if they go. They are going to have to spend time gathering and confirming intelligence.
They dont know enough about Molly to Leeroy Jenkins it either, besides a long list of heavy hitters that end with "And they died".
Arianna was a Duchess, and according to Changes, she was just under the Lords of Outer Night in status and presumably power.
Daughter of the Red King, even if I doubt she's his only progency.
If just Molly and Seeker could take Arianna and her entire retinue in a handful of minutes and with sufficient force superiority as to leave the plane largely intact? They need a lot more information before risking more vampire elders; minions might be easy to replace, but elders arent.
2)They dont have the spare forces.
The Red Court are still at war with the White Council and its allies.
They really dont have that much to spare at the best of times without uncovering something that might get shot or stabbed or bombed or nuked. Opening a second offensive front is strategically questionable.
Worse, they suffered a major defeat, with personnel losses less than six months ago.
The occasion of Molly being rescued from Arctis Tor coincides with a major battle with the White Council, where the Reds got jumped by Summer Lady Lily and the Summer Court's forces. Thats where Morgan killed a Duke and two Counts, and came within twenty feet of stabbing the Red King himself before the dude fled.
That points at significant military losses among the high nobility, who also serve as their military commanders.
And you presumably cant replace a vampire elder by going out and biting some rando.
Add to that internal political instability from the loss of high nobility.
Arianna is the second Duke/Duchess level noble to die in the last six months, in addition to at least two Counts and other high nobility, and thats going to exacerbate jockeying for internal position in the neofeudal Red Court.
Everybody of high enough visibility to be a significant target is going to be beefing up personal defenses. They shouldnt have the spare military force. Probably. And mercs willing and able to take the job of going after Molly in Chicago will be few and far between after the stories of just who they are supposed to go after get around.
3)They dont have the logistics.
They've spent the last couple years pissing off both major Fae Courts by warring in Faerie with impunity, and bringing Outsiders there, which is in part why surprise!Summer Court army happened to them in June.
Thats about to get worse.
Mab just finished a significant purge of Winter, and the Winter Fae are much less distracted by internal isues.
Which means that the Red Court's days of unimpeded freedom of access to the Ways of Faerie more or less with impunity are about to come to a screeching halt. Not to mention that with the end of the year approaching, Winter's power is waxing.
Coming north would have to be in the real world.
Risking significant forces with no safe route of retreat, and largely precluding the importation of demons or Outsiders to attempt to even the scales. In the same city as a Knight of the Cross and the mad wizard Dresden.
And as Chicago is basically Fae central, with the sheer density of Fae and fae interests in the region that implies (remember, Dresden called on a quarter million wyldfae alone in Chicago in Battleground), so whatever they do will make it back to the Queens. Which brings us back to:
4)They have treaty obligations under the Accords
Sending military forces or agents of any sort to Chicago would be an open, flagrant breach of an Accords-certified agreement they made in Death Masks to keep their forces out of Chicago after Duke Paolo Ortega lost his duel with Dresden.
And doing that would give Mab casus belli to.....chastise them for it.
Arianna tried to be clever and deniable, and we still found out and instead of making a legal case, killed her for it.
They probably dont want to draw attention or scrutiny to that before they've had the opportunity to try to scrub her tracks, especially since this is the second time in six months that Arianna has meddled in the Chicago area; she was canonically the top bidder on Madrigal Raith's attempt to auction Dresden on Ebay in June(Proven Guilty).
Which suggests that she was probably the Red Court noble who was overseeing the whole Red Court angle of the Skavis/Madrigal plot aimed at Molly, Cauldron and the White Court.
Basically, think of it this way: Seeker's stomping grounds are in the southwestern US, within a couple hundred miles of the US-Mexico border. If he, who is not an Accords signatory AFAIK, is not worried about the Reds bringing enough force into his territory to threaten him, I significantly doubt they can afford to come all the way northeast to Chicago in the next week or so.
They are going to put together a response to try and get back at us. Whether by themselves, or lending someone else support.
But I am reasonably sure its not this year. Might not even be in the next six months; Dresden killing Paolo Ortega didnt draw a military response for at least half a decade, and the Reds are still at war with the White Council.
5) Arianna's death has royal political implications
Also there's the additional political dimension that canonically Arianna Ortega was trying to build enough of a power base inside the Red Court to overthrow her father by the time of Changes.
Because according to her, while she loved her father, she believed he was a blood junkie and losing control of his appetites(true) and no longer fit to lead the Red Court, and should be replaced by another Night Lord.
For the good of the Red Court.
In killing her, we did him a personal favor in securing his position.
And also prevented the potential replacement of the currently reigning Red King with a new, more effective king and war leader, thus doing the White Council a favor.
Of course, Molly doesnt know any of this IC. Yet.