My honeymoon was in a hotel 30 minutes drive North of Mombasa on the coast of the Indian Ocean at Bamburi Beach. It was amazing.
I reckon if you use a hotel as a base for you and the family you'll have no problems. You can get good quality trips to Tsavo East Safari Park from the guys on the beach. Our trip was superb, it lasted for 2 days and we saw - antelope, elephants, leopards, buffalo, lions, gazelle, etc etc. Longer trips and sea trips are also readily available.
the food was good, the hospitality was great, the weather amazing - I can't recommend it highly enough.
Lesser known tip for avioding the runs in Kenya - don't drink anything from a coconut shell especially if its free.