We tend to find that ski holidays come in around £1k per head. Sometimes more if we've splashed out on accommodation, sometimes a touch less, but not much.
We always DIY, but even without factoring in travel, you're looking at £200 pr child for ski school, and an average of £200ish per person for passes for the week.
February half term is notoriously the most busy. We usually go at Easter, but due to clashing commitments next year are going in February half term instead, we've already booked our lessons, so if you want to do that, jump on it soon.
For us, the cheapest accommodation we've ever found was a 2 bed apartment in Arc 1800 for £280 for the week, last Easter.
It's a crude question, but what's your budget? As affordable could mean a range of things.
A good suggestion above is to rent further out and drive in each day, which will reduce cost but increase faff and also commits you to eating out every day, whereas closer accommodation may allow you to go back for lunch. Feeding six of you somewhere like France every day, you'd probably find it cheaper to have an apartment close by. And if you go for morning ski school, the meet time is usually around 0915 to 0930.
Sunweb often have good deals.
It's working out where you're willing to compromise.
Are you happy with an apartment where some of you sleep in the living room, or does it have to have separate bedrooms? Walking distance to lifts? Or ski bus or drive?
Will you fly drive or will you need transfers?
These are both on Vrbo for February half term (starting Saturday 15th) for £513 for the week. Both are about a 20 minute drive from La Plagne, which gives you an idea of the price difference.
Download the Vrbo app to look at this great place in La Plagne-Tarentaise. https://t.vrbo.io/w0x0qtipCNb
Download the Vrbo app to look at this great place in La Plagne-Tarentaise. https://t.vrbo.io/mhjBDZrpCNb