The South Island is spectacular. Personally, I prefer the west coast to the east coast, the former being more rugged with sensational rainforests. There is much to see north as well as south of Fox Glacier. If you are looking for an interersting place to stay, I highly recommend Dr. G. McSweeney's lodges at Lake Moereki and Mount Cook (http://www.wildernesslodge.co.nz/) . They are expensive, but worth every penny. I stayed at Lake Moeraki, which was an amazing experience, especially trekking through the rainforest to the Pacific Ocean to watch the world's rarest penguins. If you change your mind about Kaikourra, there is a convent nearby that has been turned into a small hotel. The owners, a New Zealander and his French wife, are terrific people. An evening at the hotel is a pleasure, and quite reasonable.
I note that you will be going to Wanaka. It's in Central Otago, where there are some very good winemakers, some of them doing interesting things with Pinot Noir.
Driving is an interesting experience. The terrain is rugged and almost all of the roadways are two lanes. Every once in awhile, there is a third lane for a short period to facilitate passing. Truck drivers are very good about slowing down at these three lane sections to let cars pass. Bridges are one lane and there is a right of way system. The bridges are for both trains and cars, meaning that when you cross a bridge, you drive over the tracks. You will certainly find that your driving skills are put to the test.
One comment about Milford Sound. If I had it to do over again, I would give it a miss. It is jammed with tourists and not really that big a deal. There are more interesting places. I might think otherwise if I was going to hike in the area.
Also, consider Stewart Island if you are a naturalist.
Regarding your daughter's interest, my understanding is that Lord of the Rings was shot mostly on the east coast some distance from your apparent itinerary. I can see why the film-makers would do it on the east coast - there is much less rain there. Bring a good raincoat. You'll need it (see the word "rainforest" above).
It's a marvelous country, with marvelous people. You'll have a great time.