I don't have any children, but I was a child myself when the Amiga was arguably in its prime. Games I remember loving from back then:
Zool 2
Cannon Fodder - hmm, maybe not appropriate depending on the age of your children :-)
PP Hammer
Lemmings 1 and 2
XTReme Racing
Nebulus - I really think your children will love this one!
Superfrog
Pinball Dreams
Pinball Fantasies
Obstickle
Megaball - you'll like this if you like Arkanoid
Many more I can't think of at the moment, and also I got many, many (many) hours of enjoyment from playing PD games downloaded from Aminet, and also from cover disks/CDs of Amiga magazines (most of which are probably also available on Aminet). You should encourage your children to look through the games on Aminet, download any they like the sound of, and try them out! Half the fun is discovering the gems. You may download 20 games and find that you don't like 15 of them, but the remaining 5 will give you lots of enjoyment.
--
moto