You must add
DDP to your
DVC reservation at least 48 hours before you arrive and pay for it at check-in.
You cannot pick and choose how long to add it - you must get DDP for the length of your stay.
You're issued dining credits based on the number of nights you stay, not days, so there isn't any reason why you would have to use credits on your arrival date. If a party of two gets the regular DDP and they stay five nights, when they check in they get a total of 10 TS, 10 CS and 10 snack credits to use in any combination until midnight of their checkout date.
You shouldn't have any problem using all your credits even though your arrival is late.
DDP is NEVER tied to park tickets for anyone. Even package bookings allocate DDP credits based on the number of nights you stay at your resort.