It's impossible to say you can definitely see the Big 5 anywhere as you really don't know what you will come across. "I would have thought that an unfenced area would mean less sightings" in the larger reserves the wildlife moves around enough that they aren't tracked every day, only in a really small reserve you might be able to do that but why pay to stay in safari park? It's on interesting debate as even greater Kruger is fenced but it is a huge area so feels more authentic.

But with 3-4 nights you would hope to come across plenty of great sightings in any of the bigger private reserves. Sabi Sand reserve is good for a chance to see leopard close up (they are very habituated) but it might be easier to see cheetah in Thanda, but again there is a lot of luck involved in what you happen to see on any day/drive.

Closer to Hoedspruit airport is the Balule reserve, for example Naledi Bush Lodge has a 2-bedroomed unit and has great drives. Lots and lots of options. A safari agent can help find a lodge good for your children and help with packages including the transfers etc that can be better than the rack rates. Fedair and Airlink do the lodge link flights, but I don't think you can see rates online as the lodges / agent will quote.