On a recent trip, I didn't see any of the $2.69 mugs available.

I think if you buy a $5 plastic mug in the gift shop, they will refill it for $2 + tax.
Resorts have no refillable mugs, so you can't refill them there.
BTW, if you just want water, any drink stand can fill up your water bottle for free. I usually ask when they're not very busy. You can also refill it from the water fountains. The drink stands seem to have colder water, though.