Yes, we have driven to Italy and S of France many times with small kids, and more recently with teenagers.
How small are the children, what time of year are you going, and have you decided which route you'll take?
My tip would be to do as much of it as you can overnight, or late night and early morning, and share the driving. In car DVDs are a godsend too. We don't normally allow them, but it keeps the kids quiet for ages on European motorways, as do audio tapes.
Frequent stops for running around and toilet, and take lots of food and sweets, partly to alleviate the boredom, and partly because motorway food is just as expensive there as it is here.
Also, if you plan to drive through Switzerland you'll need to pay road tax. Don't wait until you get to the border on the motorway, realise that Switzerland don't use the Euro, and have to pay a fortune in committion to buy some Swiss francs!
If you plan to do an overnight stop Formule 1 hotels are great. Very cheap, and clean, and always situated near a motorway junction.