Good question --- and I don't claim to definitively know the answer, which might depend in large part upon whether a resort is also available for occupancy by the general public by openly offering rentals, in which case applicable ADA law may very well require acceptance of legitimate, certified service dogs (such as those assisting the blind, for example). If a timeshare property is entirely private, with no public access and no rentals offered or available to the general public, ADA laws may not apply.
"Emotional support animals" are essentially just pets, with no legal standing or recognition or any ADA status at all. Pets of any kind, size or species can be (and usually are) completely prohibited at all times from most timeshare properties.
Just my own personal observations, not intended or presented to constitute legal advice.
KC
