What is your question? I'm having trouble parsing it.
(If I were to guess, it sounds like you are referring to DDP, not BDP, and wondering if you have to pay for the day of use that your mother will not be there for. If that's your question, the answer is yes, all guests must have the DDP for all room nights.)
Yes, Tara is correct. We went for 7 nights and our Dniece was only with us for 4, but we had to pay for the 3 of us, for all 7 nights. We used the extra dinner credits to do Signature dining, but we didn't use all of the counter service credits.