The current valet parking rules at WDW apply to all of the Disney Deluxe hotels (Animal Kingdom Lodge, Boardwalk, Contemorary, Grand Floridian, Polynesian, Wilderness Lodge).
There is a daily charge of $6.00. The first hotel each day, which will collect the money, will hang a color-coded and date-stamped tag from the mirror to show payment has been made. This allows re-use at that, or any other hotel, on the same date.
If you have a state-issued hang tag (blue or red) or HP plates they willl waive the charges. I am not sure of tags from other countries, but they will normally go out of their way to assist. I have also seen that they will waive the fee if there is a wheelchair or
ECV involved; however I have been told by some valets that it is administratively easier if there is a hang tag in the car.
As the Swan and Dolphin, as well as the Hotel Plaza Boulevard hotels, are not Disney owned and operated the rules may be different. However I do recall that at both the Dolphin and Grosvenor they did waive the valet fee with my hang tag.
Please be aware that the valets have always been a"tip position", similar to bell staff and full-service rtestaurant servers. I have known several of the valets (especially at the Contemporary) for many years. They say, and the valet tag clearly states, that no part of the fee goes to the valets. Since the policy when into effect a few years ago, they have taken a hit on their income.
I will tip BOTH when I drop off the car as well as when I pick it up. Normally I will tip the valets either $1.00 or $2.00 depending on the weather and other conditions if loading or unloading the ECV is not needed. If the valet does the loading/unloading of the ECV and also the disassembly/assembly I will tip $5.00 instead.
Over the years I have had a few times when there was need to load or unload the ECV and I did not get any assistance from a valet. In those rare circumstances not only was there no tip, but also a discussion with a supervisor.
This answer may be more than you wanted, but I think it does cover everything.