Hi there. I'm the head of one of the international schools in Kampala and parent to an 11 year old. There are several really good pools in the city. The school I lead has a pool and club house which becomes a leisure facility from 4-6pm on week days and all weekend. It's free for RISU families and very cheap for everyone else. Lifeguard, sun loungers, children's play ground, basketball court, good affordable food and an underused pool table, dstv and bar.
There is Speke Resort not far away with a close to Olympic size pool, stables and a marina.
Uganda is landlocked, so no sea. But the Nile is about 2 hours drive away where there is kayaking, quad biking and white water rafting. These are more 'treat' activities as they are too far away for week days. Swimming in lake vic and rivers usually carry bilharzia possibilities, but many residents just ensure they take treatment following exposure and still get in for rafting etc. .
Speke also has good open spaces for bike riding for younger children.