Why do you need a multiple entry Visa for Kenya?
The 'multiple' Visa is used for certain 'business' only and must be obtained prior arrival.
If 'as Tourists' (for your family) who will also be visiting Tanzania or Rwanda or Uganda and then returning to Kenya... they can use the Single entry form which is good for term of the Visa (about 3/mos). This would be the same form as used for you only.
Here's link to form from the UK High Commission. Prices shown are in GBP, but payment in USD is USD$50/person (children included). Photos are NOT required if/when purchasing on arrival... they'll have your passports; agent will take your photos and fingerprints; place Visa in passport.
Be sure to have sufficient blank pages (2) for Kenya and for any of the other countries (believe 1/pg Tanzania and the others). And, minimum 6/mos available before expiration of passports.
Edited: 2:23 pm, November 30, 2012