The thought occurs that if Kymai can hold out for three years at present, we can work on a slightly more involved plan.
What I'm thinking is that if we can settle the Dauni issue in a single campaign season, that still leaves us with two years to deal with the Kymai situation. Which can best be accomplished, I think, by a combination of two things: a campaign of raids against the Oscan homeland (i.e. the Samnites) specifically targeting their food supplies and store of wealth all in one go by stealing their livestock, and removing the women and portable wealth of Kymai to another location.
At no point do we engage the Oscans in a straight-up field battle. Our goal here is simply to disrupt the siege and thus buy more time to evacuate Kymai, and to make the experience as miserable for the Oscans as possible. Ideally, if we can somehow completely evacuate everything but fighting men and rations from Kymai, we can then offer a parley with the Oscans that lets them know there's no longer any actual profit for them in trying to take the city and get them to abandon the siege for long enough to also evacuate Kymai's remaining fighting men to their new homes.
Now if we want to be real assholes, we can try to find some way to use the Samnites against the Dauni. Best bet there would be to start saber-rattling along the border and encourage the friendlier Dauni cities to make noises of serious discontent, then once the Dauni king moves soldiers in our general direction we let the Samnites know (via Peuketii intermediaries, most likely) that the cities of Auscula, Vibini and Aecae are all ripe for the plucking. With the Dauni cities most likely to be problematic for us crushed, including the king's own city, bringing the rest under our sway should be easy. Especially when we can then offer protection from marauding Samnites.
This would also draw off some of the potential reinforcements for the Oscans currently besieging Kymai, making that situation a bit easier to handle as well.