You can't get the dining plan if you're using
DVC points to stay at a non-DVC resort. However, since you're talking about a value resort (at which you can't use DVC points), you'll need to either make a room-only reservation (which can't include dining) or buy a Magic Your Way package (to which dining can be added).
Your DVC status won't have anything to do with getting the dining plan there. To get it, you'll have to buy the same Magic Your Way package that's open to the general public. That package, unfortunately, will need to include at least a one-day park ticket. Also, everyone in the room must be on the exact package; meaning same park ticket, same arrival and departure date, and same dining plan. As already indicated, the other down side of the Magic Your Way package is that you can't apply room discounts (such as AP) to the package. You're always paying rack rate.
If you're planning to purchase an annual pass or other ticket, you can upgrade the one-day base ticket from the package. Magic Your Way tickets expire 14 days after their first use unless you purchase the 'no expire' option. However, even without the no expire option, if you never use the first day, that 14 day countdown never starts. So, even if you already have an AP or tickets for this trip, you could still save the package tickets for use during your next stay or toward your next annual pass.
Also, don't forget you'll be on two different dining plans during your stay. You'll need to use all the credits from your DVC
DDP before 11:59 PM on the 11th or you'll loose them. They won't carry over to your weekend stay at the value resort, even if you buy another dining plan there.