Ticket validity is not linked to your hotel reservation. So presuming your ticket does not have the No Expiration option, they are valid for 14 days from first use, even if that extends beyond your check-out date.
The Front Desk of your second resort *should* also be able to move the ticket from your first room key to your second, but be prepared for it to take a little time.
As for the Dining Plan...
To get the DDP, you must book a vacation package that includes room and park tickets. The minimum number of days it usually 1 or 2, depending on the package. But if you're getting 8-day park tickets, it's not economical to get them as 6-day and a 2-day tickets. If you must get the Dining Plan on your second reservation, get tickets for your entire stay on your first reservation, book the minimum number of days on the tickets for the second reservation, and then *save* the tickets on the second reservation for use on a future trip. If you don't use them, they will remain valid forever. (And when you do go to use them, you can upgrade them to whatever ticket you need at that time)
But if you get tickets with your second reservation, you will not be able to move the tickets from your first room key onto the second. And you *really* then have to make sure you don't mess up and use your second room key for admission into the park, because then it screws up the whole save-the-second-tickets-for-use-later scheme,
And Dining Plan credits expire at midnight at the end of your checkout day on each hotel reservation.
-Rob