Having transferred frequently between the Dolphin and Disney-owned resorts consecutively over the past 14 years, I've NEVER experienced any problem. I've transferred both to/from, without a hitch. I know I've seen this matter posted in the past, and have always posted my experiences. I even mentioned this to the Bellman at the Poly, as he was loading our luggage to transfer it to the Dolphin. He laughed, and said, "Misconceptions are rampant in WDW. We have a symbiotic relationship with the Swan/Dolphin. We do not transfer luggage to any property OFF-SITE, but the Swan/Dolphin are ON-SITE resorts, therefore, part of the Disney resort Family!" I reiterated his sentiments, acknowledging the other perks which the Dolphin/Swan patrons are entitled to enjoy. Only one, "universal charging privs" are exclusive to Disney-Owned properties. Otherwise, the Swan/Dolphin share every other Disney Resort PERK, including luggage transfers! Finally, no discrepancies on this issue.
I recall a little-known aspect of the old Disney Institute. DD would sign-up for the day camp classes, taking behind the scenes in the AM, and face-painting in the pm (or other classes). For the cost of $95.00, she would spend the entire day (8 am-5pm) w/counselors and enjoy all the magic of DISNEY. This included her lunch and snacks. We called about the transporation, since we were staying on property w/o a vehicle. The counselor informed us most persons are unaware of the "TAXI VOUCHERS" available at each resort's guest services desk" for this purpose. We used a voucher to travel to the institute, and then obtained another from the BW (We were not staying there at the time, just enjoying the sights) to travel back to the Institute and retrieve our daughter. Then yet another, to travel back to our resort.
She also informed me if our daughter was at one of the child-care centers in any resort, and we were at a resort restaurant, etc., we could obtain a "Cab voucher" from the guest services desk to travel directly to the desired location and reunite w/our child. These "vouchers" take care of the cab fare 100%. We have not used the vouchers in years, and are not even sure if they are still participating in this feature. Yet, it was a wonderful, convenient "perk" during many of our Disney ventures.
Also, you do not have to be "staying" at a particular resort, to take advantage of their child-care facilities. While we were at the Dolphin, (years ago) DD wished to try the BW child care facility (we visited it whuile perusing the grounds). We asked the BW management, and they informed us it is not a well-known fact, but any Disney Guest may use the child-care facilities of ANY resort. She had a splendid time, and returned several times.