You won't be able to do this unless you have a
DVC reservation or annual pass.
You can't add
DDP to a room only reservation. Unless you have an annual pass, you must convert that reservation to a room/tickets/dining package, and you MUST buy tickets in conjunction with the reservation where you wish to use the dining plan. Even if you bought tickets with your first stay at the Yacht Club, you'd have to buy them again when you switched to the Polynesian. Of course, you could buy 9 day tickets at the Yacht Club and then a one-day ticket at the Polynesian, but if you already have tickets you probably won't want to lay out cash for another one-day ticket, unless you can hang onto that ticket and use it for admission or an upgrade on a future trip.
You must purchase some sort of ticket in conjunction with your checkin at the Polynesian in order to get the dining plan with that stay.
You'd have to do the math, but with a stay that length it might be workable to buy one adult annual pass and use it to book the Polynesian stay as a room/dining package, no tickets. I would make sure there is availability on the room/dining AP package at the Polynesian for your dates first. You can book the package without having the annual pass, but you'd need to present one at checkin.
My other suggestion is to buy length of stay tickets either at the Yacht Club or before you get there, and put a one-day ticket on the Polynesian reservation. One day tickets never expire and can be used to upgrade or pay for new tickets in the future.