Technically, no. The
Disney Dining Plan is based on the number of NIGHTS of your stay, not days. So if you were to check into Pop Century on Saturday and stay there Saturday night, Sunday night and Monday night, your
DDP would include three snacks, three counter service credits and three table service credits. These credits expire at midnight (well, 11:59 PM, to avoid confusion) Tuesday.
Then on Tuesday you check out of Pop and into Animal Kingdom Lodge and stay there Tuesday night, Wednesday night, Thursday night and Friday night (then go home Saturday). You again purchase the DDP. This time you get four snacks, four counter service credits and four table service credits. These credits expire at midnight Saturday.
Therefore, in your seven night total stay, you get seven "sets" of credits. Not eight, you're not doubling up anywhere.
That's the good news. Now the less than desirable information: In order to be eligible for the Disney Dining Plan, you have to purchase a package. What constitutes a package is a room-plus-park passes reservation. Your package has to include the same pass for each person on your reservation; this pass can be upgraded later and does then NOT have to be the same for each person.
The problem the OP is going to have is that they will have to purchase TWO packages, each with at least a one-day one-park pass for each person on the reservation.
Note that DVC members, or Guests staying in a DVC Resort using points, can book the DDP without having to purchase any park passes.