Camden NSW to Darwin

To help you out for the last part, 7ks north of Tennant Creek is the Pebbles. It is free camping and plenty of room for vans. And you can get phone coverage.
As for Katherine, Edith Falls just north (42km) great for kids you can walk the Katherine Gorge from there.
Cheers Andy

You can always spend more time "everywhere" and most places you compromise, but I'd consider one day less at Port August and a full day (2 nights) at Coober Pedy

I think you mean the Olgas instead of Bungle Bungles, and 2.5 to 3 days is adequate for Uluru & The Olgas. Can do it in less, it will allow you to tick it off the list but not necessarily appreciate it
Kings Canyon is a Full day (+ half day getting there).
Kings Canyon to Alice is 2 days without really doing the West Macs any justice, (I think you could take another day in the West Macs, staying at Glen Helen "resort" or Ellery Big Hole or Ormiston).
Sorry I'm inexperienced north Of Alice.

For our family, your itinerary looks a little rushed, not enough time to relax, kids need some downtime where they can clown around, play in the sand/mud. You also need to factor in a flexible lay day or 2 in case something goes wrong with the vehicle or someone's health.

Search on member "MotherHens" Blogs, there are some great ideas for those areas. Admittedly they had more time and mightn't have had kids but it is a really good guide.

Mark

Make sure you buy all your supplies from Coober pedi iga before going on to Uluru as everything is very expensive there and stay at big 4 in Coober

With only five weeks and travelling with little ones, I can only suggest you spend more time enjoying yourselves and less time driving. Do you need to go all the way to Darwin this time? You will miss out on so much.

We spent five weeks in and around Alice Springs in 2008 and returned in 2009 to continue to Darwin over several weeks.

Do you need to have a structured plan? If not, travel at leisure, spend more time where you enjoy it and see places thoroughly instead of burning fuel to head up a bitumen road just to cross the country. That way you can turn around when you have enough time to make it home, even if you haven't gone all that far. At least you will have had a relaxing holiday and seen a whole lot more while not just driving long distances.

Camden to Mildura, that's a big drive. You'll see nothing in Mildura if you are off to Broken Hill the next day so why go there? You'll save 200kms by driving straight to BH via the Barrier Hwy. Split the drive by staying in Nyngan or Cobar.
Broken Hill and Silverton are interesting places, tick.
Two nights in Port Augusta? Phttt....You've driven past the Flinders Ranges
Port Augusta to Coober Pedy will take most of the day, then Coober Pedy to Yulara is a big drive. You won't see much of CP. CP is fairly unique with interesting shops and displays. Tick.
You've got the Bungle Bungles in there. They are way over near Halls Creek in Western Australia? It's a longish drive from Yulara to Kings Canyon (3.5 hours?) so you'll need to stay at Kings Canyon to be able to do the walks. It's a long drive from KC to Alice as well, maybe 4.5 hours.
Two weeks in Darwin seems a waste when you have world heritage national parks near by. Darwin is ok but in my opinion a few days is enough.

If it was me, I'd be cutting it short, stopping at Alice Springs and not going any further and doing the Flinders Ranges on the way. Anywhere you have a 2 night stay above really means you have 1 full day to see the place. You can't see the Rock, Olgas and Kings Canyon in 1 day...well you can see them as you drive by. :-)

How far is it? Keep in mind it's around 28 hours driving time from Sydney to Alice Springs. That's 4 x 7 hour days in the saddle not including breaks for the trip home. Don't come home needing a holiday.

I think it's all realistic for both time and distance while being enjoyable. You might find you only spend a week in Darwin and use the time to stop at alternate places on the way back such as litchfield, Edith falls, mataranka, etc.