If you must book packages with tickets to get a dining plan, and you want dining plans on both the reservations, you will have to purchase tickets on BOTH reservations. Because Disney's multiday tickets are top-loaded and get cheaper the longer you stay, this can end up costing you a fortune if you split your ticket allotment to match your resort stays.
You can buy the minimum ticket on the second reservation and then save it for later use.
I think if it's only one day you are far better off paying for the food, unless you're DVC or eligible to book a ticketless package.