Defintiely go with a UK tour operator like those I've mentioned then. Half term local ski schools can be really crowded but some of these have their own exclusive groups with English speaking instructors. tbh you may not have an awful lot of choice for half term even now, especially if you require several rooms and dedicated childcare. Igluski.com will do a search of various operators to your specifications and may throw up some specific family orientated resorts.
UK operators tend not to have a smaller choice of resorts for Austria compared to, say, France. Mark Warner have a dedicated hotel in St Anton in Austria, which is a good resort and the hotel is fine too. I haven't used the childcare but looked perfectly nice. It won't be cheap though, specially not over half term.
We tried Obergurgl last April - still buckets of snow and less crowds - just lovely. Had a 5 year old and 7 year old - ski school was fantastic with excellent English spoken. The resort is small but a fast gondola links to Hochgurgl and there is skiing to suit all levels.
If you want a small, quaint, genuine Austrian skiing village - you can't beat this place!