As cdrn said you can accomplish this by booking 2 reservations but you do run the risk of having to switch rooms as you will have to check out/check in at the end of the first stay.
Since DDP must be purchased as part of a package the most economical way to do this would be to book the first 3-4 days with the ddp and the second stay without it, booking your tickets with your first stay for your entire disney trip. The dining credits will expire at midnight on the day you check out from the reservation you booked with the ddp.
So say something like this -
Res. 1) MYW Package June 14th - June 18th, POP Century, 2 adults 1 child, 9 day park hopper passes, Dining plan
Res. 2) Rooom only Ressie June 18th - June 23rd, POP or any other resort.
Lots of people like to make split reservations like this since they then get to try out different resorts. Your tickets are good for 14 days from first use (or forever if you purchase the non exp), but as I said your ddp credits will expire on midnight when you check out of that first reservation.