I'd go with Frank's advice, on flight or ferry.
If that's not for you, with kids, and especially with four of you, I would recommend traveling by car (or like Frank said, Ferry).
Train can be very inconvenient from Venice to the Dalm. Coast (loooooong rides, inconvenient times)... but if you think you can survive 15 hours on a train with kids... :)
Bus is a little better, but still looong, times aren't that great, and there's usually only 1-2 a day.
Car rental in Venice is easy, it's right at the edge of the city, no mess to drive through. If you're returning it to Venice, you can probably get a great rate.
Most roads in the area are easy to drive, and a GPS and map will get you anywhere. Most car companies also include the 35EUR sticker for driving on freeways in Slovenia, which is nice. Some do charge and "Eastern Europe" driving fee, so it's something to ask about.
How much time do you have? There are some nice thing to see along the way...