When are you planning on going? My recommendations might change depending on whether you are going in summer or winter!

I second the advice to get out of Santiago. It's really just another big city with lots of malls, cars, and pollution.

Our favourite family vacation in Chile was our trip to San Pedro de Atacama. We loved the Tierra Atacama, although our kids were a bit older than yours (6 and 8) when we went. They have family suites with separate bedrooms for the kids. It is all-inclusive, and because we had kids they basically assigned us our own travel guide and van for our hotel trip, rather than having to share with other guests.

We also loved Easter Island (Rapa Nui); the Explora is pretty spendy, but there are lots of nice cottages to rent as well that are quite reasonable. A lovely, relaxing holiday and the beach is fun (although the waves would be pretty rough for toddlers).

La Serena has a beautiful beach although can be a bit chilly in the mornings. We quite liked the Enjoy Hotel.

For the novelty of it, you could stay at the world's largest swimming pool. http://www.sanalfonso.cl/ingles/ It is very easy to get a time share rental outside of peak times (January/February).

The lake district is lovely - I would recommend staying in Pucon as there is lots of stuff to do within walking distance and the roads are often jam packed making it an ordeal to drive anywhere.

If you have any specific questions, please let me know.