In general, the majority of lodges will not allow children younger than 5 to go on the long adult game drives. Each lodge, however, has their own rules regarding the age they will allow children on game drives, and you should check exactly what your children will be able to do at your chosen lodge when booking - finding out that your 8 year old cannot go out to see the animals at the lodge you have chosen when you arrive can ruin your whole family's stay if you did not know this in advance.
There will always be babysitters on hand to look after children during game drives if they are not allowed on the game drives.
If you really do want to share the safari experience with your little ones, you can ask the lodge if you can hire a Land Rover for a day, and the ranger will only take you and your family out on your own game drives.
This will be an extra cost over and above the rate that you would normally pay, and whilst the lodge will do everything they can to accommodate this, they all do state that they cannot guarantee this service - purely for the reason that each lodge will normally have just one 'spare' Land Rover - and if one of the vehicles that is due to take out the other guests breaks down, then the spare vehicle has to be used.
Alternatively, in East Africa, using a private driver-guide is ideal for families, as not only does it bring the cost of the safari down (as you are on Full Board rates and you can avoid having to pay for a return flight for each family member), but there are obviously no age restrictions imposed.