Kevin:
You should have no problems getting direct Disney transportation to either of your dining locations.
To travel from the Yacht Club to
Disney's Hollywood Studios, you only have to walk out the back lobby doors and follow the side walk to the hotel's marina area, specifically looking for the little lighthouse. There, you can catch the boat for the roughly 20-minute ride to the park. Be aware that you may have to wait up to 15 or 20 minutes for the boat so the transfer could take a maximum of about 45 minutes. (You could walk to DHS along the canal in about 25 minutes.)
You'll want to catch the bus at
Animal Kingdom that services the Swan and Dolphin hotels. You may share the bus with guests from the Boardwalk hotel and even possibly the Beach and Yacht Clubs, but you'll find it a 25- to 30-minute bus ride. Again, keep in mind that you may have to wait on the bus, but it will only be 20 minutes tops.
Wishing y'all a magical vacation!
Whitney