Cortina D’Ampezzo

Ok, so by ski parks you mean the ski resorts/areas. Hmmm....I love your confidence re:winter driving long distances in Europe. Driving on the American highway system and driving from Milan to Austria are two very different experiences,especially when driving over the mountain passes, the weather can change very quickly. Re: night skiing you need to check their opening, some resorts only do one night per week, some more. Do your research re:skiing resorts/driving routes/distances first, especially when travelling with the kids. Still think you are trying to cram too much in for a very short period to it being enjoyable:) Take care!

you are absolutly right, i just go by what the map show, from Linate Milan to Innsbruck, Austria is 5.5 hours, with gas stops and bathroom stops lets say is 7 to 8 hours, will you agree ?

Yes, that's a realistic, if you want to ski in SkiWelt area that's of course further from Innisbruck. There's 8 villages for access to the area, if you look at Skiwelt website you can read about them. I like the area, have stayed with children in Söll & Ellmau before.

Still think with the limited time you'd be better based in one ski area closer to Milan (i.e. in Italy), either in Livingo or somewhere in the Dolomites Superski area or in Madonna di Campiglio. To have time to enjoy skiing, food, atmosphere.And never sure about the winter weather, could be brilliant, could be snowing on the dates you want to go :)
To get more info and a feeling about the different areas have a look at Skiwelt area website, also Dolomiti Superski or Campiglio Dolomiti or Livigno.

When planning bear also in mind that most accommodation is on a weekly basis in the winter but the bigger hotels should be able to accommodate shorter periods, all depends on where you are staying.

I was just thinking that Cortina might actually work for you too for a short trip if you'd like to experience the place. The scenery is beautiful like anywhere in the Dolomites and now with a Skyline gondola there's a direct access to Cinque Torri and Lagazuoi area and beyond.

Thinking of the children and their abilities Alta Badia could be a good area but also Madonna di Campiglio. Hope the above is a bit of help but of course it's all my personal opinion based on taking the family skiing over many years, the other people might have other suggestions. Good luck, there're so many ski areas to try out:)