Why is Switzerland a must? You'll be in Europe again, why spend all that time on the train when you could see a country that borders the first one you land in? Switzerland is also extremely expensive. It takes additional time to travel around Switzerland, BTW. Don't add a fourth country, it's a mistake.
It's hard to choose between a city (Amsterdam) and a country (Italy.) Someone who has studied art would certainly choose Italy. But plenty of fabulously important artists worked in the Netherlands. My wife and I made our first trip to Europe as a week in London and a week in Paris (before there was Eurostar.) The second trip was Rome/Florence/Emilia Romagna/Venice over two weeks.
I usually recommend Amsterdam for the first trip for people who are slightly nervous about going to Europe, including people who have been to England ten times because they are uncomfortable going to places where strange languages are spoken. (I'm not making fun of you, just trying to give the flavor of the recommendation ... You didn't say anything about likes and dislikes!) But I think you should add Cologne and Antwerp before training to Paris, and flying home from there. Note that Antwerp and Paris both have the possibilities of more short daytrips than you can possibly make in your 12-day vacation. You will NOT feel like you were stuck in one place. In any case, the developing feeling of being "at home" on a "familiar" street in a strange city is conducive to wanting to return to Europe. Try to have a local, stand-up breakfast in a very local bar, if your hotel doesn't have a basement breakfast room.
My parents took me to Europe in 1952, when I was one. The only issue I can see with the child is whether you hope to get baby-sitting for a dinner or a daytrip.