Hiya, Stuart, and welcome back to planDisney!
I'm always delighted to assist a repeat visitor, especially one who has reached out from across the Atlantic, and as the proud curator of an ever-growing magical cup collection, including quite a few Resort-Refillable Mugs, I'm bubbling over with excitement to discuss this topic!
The first step in your quest for unlimited refills will be to locate the quick-service dining location at your Disney Resort hotel to purchase your refillable mug. (Most recently, I secured mine from Contempo Café at Disney's Contemporary Resort.) Once you have a visual on your target, all that's left is to choose the color of your lid!
A 15-day vacation to The Most Magical Place on Earth sounds practically perfect, and perhaps the only downside is that, as you mentioned, refillable mugs are valid for a maximum length of 14 days. Although it is not guaranteed 'yes', I suggest speaking to a Cast Member at the time of purchase to see if there might be a possibility of extending the activation of your mug for the extra final day. Because this would be done at Cast Member discretion, you might be asked to revisit the situation on the back end of your stay, so I also suggest holding on to your receipt from the time of purchase (if not charged to your folio) in case it is needed to fulfill your request. I cannot guarantee that your request can be accommodated, but my philosophy is always that it can't hurt to ask!
A Bonus Tip: I see that you're spending the majority of your trip at Disney's Beach Club Resort. planDisney just launched a new Resort Guide video series that kicked off with your next magical home away from home - Beach Club! It helpfully walks viewers through rooms, restaurant offerings, pools, and amenities, so I encourage you to take the time to
check it out before your arrival.
While I was unable to give you a definitive answer, I hope this was helpful, Stuart, and that you'll
stop back by planDisney with any additional questions you have. We're always happy to help!
Cheers,
Lizzie