The one and only place to park in Venice, is the one-and-only Garage Marco Polo!

Your happy car will drive in here...

Of course you can easily book in advance, just phone them or use their web site, I think.

I have in fact found the web site for you Henrik:

http://www.GarageSanMarco.it/en

They have Italian, German, English on the web site. Note that their computer/payments integration is perfect (sometimes this can be a mess for parking in the area) - you can confidently and easily book online with a card, or phone them for a friendly chat.

(FWIW they have a system where you save a few dollars if you stay at one of the hotels on a list of hotels they have.)

From there ("behind" you in the photo) step over 20 meters to where you will see the vaporetto ("water bus") (a sound reminder that public transport which floats is ... public transport).

Step just past it and you can easily get a water taxi which will take you around to your hotel.

Really though, you have two kids and two adults right? Just WALK all the way from garage marco polo, to your hotel. You won't be unhappy. Indeed you will be very happy. Naturally pack very lightly for Venice, I mean to say, just a small luggage you can roll behind you (the smallest possible). (If you think to take normal full-size luggage to Venice, totally forget the idea.) (Another wonder of parking in garage Marco is that you can leave any major luggage there safely stowed in your car.)

rather than staying in Mestre and taking the train...

If you want to stay in Venice, for God's sake don't stay in Mestre - stay in Venice. The reason to stay in Venice is because you're staying there. To stay in Venice is magical. The kids will love it!

Re the other comments, There's nothing wrong with going to Venice when there are lots of tourists. That is the very magic of the place: even a flood of tourists can't take away the magic.

To stay, you can't beat Pensione Guerrato http://www.hotelguerrato.com but book early.

Note that some would suggest parking at the airport or whatever and taking a long water taxi all the way to Venice, to your hotel. I do not recommend this. It's way overpriced and just not that fun. (You think of speedboating as like in a Bond film, but it's actually just noisy, annoying and everyone gets seasick.) The small water taxi ride I outline above is fine, so as to say, you've been on a water taxi in Venice. But what you should do is simply walk, right from the beloved garage marco polo, to your hotel - it is great, your adventure has begun, your car will be happy.

The only parking I'm aware of that lets you book in advance over the Internet is at Marco Polo Airport (http://www.veniceairport.it/en/park.html). It's a good option, though; competitive prices (from 10 € a day) and plenty of services to get to and from the city (Venice Marco Polo Airport to Venice); your kids will definitely enjoy arriving into Venice by boat (the Alilaguna service is now 15 € one way).