The honest answer, plus the ages and park choices that work best with children in tow.
The honest answer is yes, with sensible planning — and Kenya is one of the easier places in Africa to do it.
Most camps take children from around six, and some from any age with a private vehicle. Below about five, the long drives are the real obstacle rather than any danger. Amboseli and Nairobi National Park work well with young families because the drives are short and the wildlife is close to the road.
Book a private vehicle if you can. It costs more, but it means you leave when your children need to leave rather than when the group does — and that single change is what turns a hard trip into an easy one.