Does this resort cater well for kids, specifically age 3, 6, 7 and 10?
They have ski schools for all ages. For absolute beginners there are easier resorts than St. Anton.
I suggest you to go to Serfaus in Tirol: www.serfaus-fiss-ladis.at/en - It is a great resort for children. And for adults, you have 200 Kilometer slopes.
Slopes in St Anton, as mentioned, are not for beginners.