If you want the dining plan for your youngest child, even though he's only staying for part of the vacation you will have to include him on your res before you arrive. Dining plan must be added no later than 3 days before arrival (or 2 days if DVC on points.) If he is 10 years or older he will be on the adult plan and you or your other children can use his extra credits for additional meals or 2 credit sigs.
If you don't want the dining plan for the days he's not there, you will have to wait and add him to your room after you arrive. You'll have to purchase his ticket separately and pay for his food OOP. If he needs DME you will have to contact them with his flight info when you arrive since he'll be arriving the next day.
I wouldn't recommend getting the dining plan for your third son for just the days he'll be with you because it would involve 2 or 3 separate reservations and the ticket requirement for each reservation which wouldn't be cost effective, unless you qualify for a ticketless package or reservation - AP, military rate, or DVC on points. And even then it seems like it would be quite a hastle.
If you aren't able to get dining reservations or don't plan to have desserts you might want to consider not getting the dining plan, especially if you are paying for it.