I would remake it for the Wii in 3D, but the time I got my mits on it, It would be vastly diffrent but with the same core.

--Storyline--
I would try and refrence other storylines to put the game in itself, make new questions, and fill in a little answers. Stick with the story, but It can be told far far far better, Probably hire some professionals. Link probably wouldn't even get to the Palace where the game starts until a hour into the game at best.

--Atmosphere effects and Graphics--
Put in alot of atmosphere effects in serious design and dark theme like MM, Leaves falling from the trees, Link gets wet, Orange sunsets filtering threw the trees. Also give Hyrule one arcecture theme, (accept for ruins) as It was just silly on TP, But even with a similar theme, the towns and buildings can all look diffrent. I would also try and put in a progression of fashion, Fashion evolves in time, but the people of Hyrule have been wearing the same weird rags forever. Also put in dynamic windows that you can see out of and light comes threw depending on the time of day. Vast open fields and towns leading up from a hilly road overlooking the sea from white cliffs would be visually stunning. The full Hyrule would be put in, from LoZ and AoL (as shown on the maps they are apart of the same land and connected.) Put in animals such as seagulls flying overhead squaking.

--Gameplay.--
I would obviously have to try and keep the basics of what made the game, the game, so The palaces would probably have the same layout as they did in the 2d game but in 3d and more detailed, probably greatly expanded upon.
But then I would want Link to interact better with the Wiimote. Since the storyline would be like 100 times longer and details, I imagine the gameplay would be too, there would be more in the palaces and more then just the palaces. The scenery would be interactive and things you do would effect events and dialogue in game to many diffrent degrees and even the ending somewhat. Characters would have alot of coversations as in Animal Crossing for example, even NPC's to draw upon that change depending on the time of the game.

--Minigames--
Here, Im a theif.
First I would want to use some of Nintendos other successes, such as the interactive nature of Animal Crossing. With that as a basic feature of the enitr e world like base but in a huge Hyrule world, the game would last far longer with diffrent and unquie events happening at real times of the year, maybe even seasons relating to the real world as in the game fossil diggin, social interactions, The Stores, sending messages to other zelda games over internet etc, though it would have to be a little more grown up and less girly.
Put in ALOT of the standard Minigames, and alot of history to the country for people to uncover.
One complain I here against TP was Castle town just seemed flat. Where as places like Defino town from Mario don't as you interact with the town alot, and adventure in the levels around it many times for diffrent things, the basic principle would be brought in so each town would have several events each to do in it as in Mario Sunshine and thats not even including the minigames.
The final point would be Majorias Mask, Add in totally the dynamic system of MM. The time, (linking to the animal crossing like feature) and people moving around actually doing jobs at certain times of the day with buckets of personality, reasoning, etc.


--Side Quests--
So many it makes MM look baron. Lots. Including a handful of epic side quests that are almost aslong and as interactive as the main storyline itself.