Second opinions that small prob better with wee kids, and remember, happy kids = happy holiday. I will throw in a different suggestion, how about a Kinderhotel?
We have stayed at hotel alpenrose in the very wee resort of Lermoos in Austria. Skiing for adults is enough (actually, I really loved it, and you are within easy reach of other stuff if you want), and it is a truly magical place for families. we went with a 1.5 and a 3.5 year old, and it was bloody fabulous. Can’t wait to go back! Many accommodation options.
http://english.hotelalpenrose.at/
It is close to Innsbruck so you can fly and then a short transfer that the hotel will pick up the tab for. it is very good value, although initial outlay might seem expensive, as all things are laid on and the child care, kids facilities, kids ski instruction, and furthermore the facilities for adults are fabulous.
kev