Hey, if you come up with some brilliant strategy where it is better for the dragons to attack during the day, have at it.
I'm just going off of the information you provide. You start by saying the dragons are ancient, then you say they know the type so will have gear/magic to aid against the breath (antitoxins and spells only last 1 hour, so they will have to spend their first actions on those), and you say one only has half HP, etc. From your OP, a party of 15th-level PCs against two ancient dragons is most likely a TPK. We had a party of 7 5th-level PCs (not including the ranger's animal companion) against a young black dragon, and that was nearly a TPK.
300-400 defenders.... so how many are clerics? How many are level 5 and can cast Daylight? BTW, the range is only 60 ft, so if they do cast it in an area the dragon is attacking, they are right on the front line and I hope they survive the first breath attacks. They won't be lighting up the night that much along a bunch of city walls. So once daylights are cast, the dragons can attack areas where they aren't affected.
I suppose the city could have low-level clerics spending hours casting Light repeated on arrows over and over in anticipating the attack. But again they won't know the dragons are there until it is too late. After all, light only sheds as much light as a torch anyway.
The dragons don't need to dispel the light arrows. If they get hit by one, they can fly to safety and have it removed (or do it themselves), even buried it if needed, and then return to the fray. Dragons can use hit and run tactics, and the archers will also be busy firing against the horde of monsters as well. Anyone the dragons kill, most won't be replaced, so one night they attack and kill a hundred or so, then pull back. A couple nights later, they do the same, but with full HP (well, if the one is a simulacrum that one shouldn't risk injury until the final assault).
But, yes, to your point, a dragon most certainly should anticipate spells against it as well and should be prepared. A creature that has lived several hundred years won't likely risk its life unless it knows the odds are heavily in its favor.
I don't know how long you've DMed or played but you asked for advice about running the battle. As a DM for nearly 40 years I offered advice on how the dragons should fight given my experience. Like it or not, that's how I see it. But I don't like it when I offer advice and others get offended by it. The point is simple: both sides should do everything to help themselves and from your statements about how much arrows would do, etc. it didn't sound like you were. Since you don't have to lay out everything, that is fine, but then I think you should expect responses based on what you do tell people.
They're your dragons, so play them however you want. I'm done with it.