In reply to john arran:
> Consider going to a smaller resort. If you're looking after 2 kids you'll have little time for your own skiing so won't be able to cover much of a big resort anyway and the costs can be hugely lower. For example there are some small and very friendly resorts here in Ariège which are great for families and cost less than half of what you'd pay in a mainstream Alpine resort.
I think it depends a bit on the age of the kids, and if they'll be skiing with you all day/in lessons for part of it and then too tired to ski.
My experience of 4 & 6 year olds skiing for the first time is that they'll not want to ski a whole lot other than in lessons - which means one adult can take off for the best part of a day if they wish. On the other hand, a 7 year who's skied for 3 or 4 seasons already will likely be skiing most of the day with parents after lessons, and as you say, unlikely to cover huge distances.
Or maybe it's only my other half who sees it as a personal challenge to visit some obscure off-piste 3 valleys away starting after lunch and still being back before lifts close!
More practically, are you likely to find good kids lessons in English in Ax? Don't have a clue, it's 10 years or more since I've been, but it only really seems to be an option in the bigger alpine resorts in my experience. So we've stuck with those whilst kids are little, with the idea that we'll start heading to smaller places once they no longer need lessons in a couple of years.