If most of the children in your group are very young, your options are fairly limited as the reality is that a longer, multi-day safari can be a bit much with very young kids. I first did a safari with my kids when they were five and two years old and although it was good I probably wouldn't do it again! Past the age of about eight or nine the safari experience gets much easier, as they'll will tolerate sitting in a jeep on a bumpy road for longer.
Do be aware that some safari camps don't accept children below the age of 12. These are normally the unfenced camps and it's done for safety reasons.
You will also need to keep in mind that you will either need several safari jeeps and to travel in convoy or a bus (and these aren't always allowed in some parks). Because you will be travelling with so many children I would suggest small safari camps which you can book out for your group alone. Some of these are more child friendly than others. Some possibiltles that I believe might work well for your group are: Maji Moto Eco Camp, Loita Hills Basecamp, and if you are interested in a Maasai homestay style experience then I'd suggest Semadep Camp, who can arrange homestays around the Masai Mara.
As for specific parks and reserves the Masai Mara area is good because there's a lot of animals to see everywhere you look which keeps children interested. Also good are Nairobi and Narok national parks because of easy access and good roads. Lake Naivasha is good for families too.
It would be easy to combine all these places into a 10 day safari and then you could maybe finish up on the beach (Lamu and Watamu are both superb for families).
