@winterrabbit
There are not many ski-in/ski-out chalets in Austria because - a) chalet holidays in general are not as popular and there are few British travel companies offering this type of holiday (compared with France for example); b) most Austrian resorts are working villages, not purpose-built concrete resorts and c) the prime locations next to ski lifts (and often in the centre of the village) are owned by big family-run hotels.
That said, it is possible to find places if you know where to look.
For example, Saalbach-Hinterglemm has numerous hotels that are no more than 5 minutes walk from the lifts (and some that are ski-in/out). These hotels also tend to have swimming pools and childcare facilities, and are of course in the centre of the village.
An alternative that you might like is an Austrian "Kinderhotel" - family-run hotels that are focussed on families with children. These have pools, playrooms, nannies, are close to the slopes or have a minibus/tractor "train" that takes the kids to ski school etc. Some are next to (or part of) working farms and the staff take the kids over to see the animals, ride ponies, pet the rabbits and goats etc.
A good starting point is to look at the tourist office websites for some resorts - Saalbach, Maria Alm, Mayrhofen, Solden, Flachau, Westendorf - there are literally dozens of places.
"Lech (specifically Oberlech) would fit the bill. It's brilliant."
It is also probably the most expensive resort in the whole of Austria (along with its neighbour Zurs) where you'll rub shoulders with royalty, film stars, millionaire industrialists and shady men whose sudden wealth comes from dubious sources :-)