In 2007, we took our daughter, then 2 years + 2 months old, to Kruger and had an amazing 4-day holiday that we all still talk about. We did not do a safari or go on a group tour. We had our own rental car (which we got in Jo'burg) and drove ourselves around, which worked out beautifully. I had packed a backpack full of things for our child to do in case she got tired of all the hours of slow driving, but that pack never got opened once. She was fascinated the whole time -- by both actually seeing animals as well as the possibility of perhaps seeing animals.
Through their web site, sanparks.org, I booked reservations in bungalows for 2 nights at Skukuza rest camp and 2 nights at Satara. This worked out perfectly for us, and I would do this again in a heartbeat. You do have to watch out for the monkeys trying to steal your food though -- one evening, we lost all our corn-on-the-cob straight off the hot grill. It's fairly easy to find out where the animals have been spotted (just ask or look at the posted notices each day), and where you see other cars stopped, there's probably animal activity there. Sure, you're not going to get the rare sights that only a guide would be able to find, but you can probably save that for a future trip when your kids are all old enough to enjoy having a guide. A fun thing that friends recommended: Several mornings we would pack our breakfast into the car & go drive to a watering hole, park, and eat our breakfast while watching all the animals come to drink.