OK, not sure where you might be going but here's a few:
ETNALAND - zoo and aqualand - with slides, cable cars, pools, dinoworld and rides (for bigger ones). V busy in August though.
FERROVIA CIRCUMETNEA - narrow gauge railway from Catania Borgo around Etna, beautiful views
ETNA CRATER - lovely drive up through cool pine forests (perfect for picnics). Etna itself is like being on the moon and quite something. You can also go up in a cable car with a jeep ride to the edge of the crater (but I don't think I'd take 2 years olds on that LOL).
CASTELLANA PARK - another great aqua park
ACQUAPARK MONREALE (PALERMO) - another one
TOY MUSEUM (CATANIA) - haven't been there but a friend told me they have shows for kids and there's lots of hands on stuff.
AGRIGENTO - is also very interesting. Big Roman archaeological area. No real facilities (except drinks). Fantastic to run around but DO NOT go in August. It is unbearably hot.
Taomina and Cefalu are lovely towns to wander round and sit and drink in cafes.