When we used a nanny: T4 Nannies, the max they could take was 4. It worked brilliantly.
However my DD's no longer used any childcare and just skied with us after lunch by the age of 5. OK, they can both ski well, but they ski all day without any bother. I couldn't imagine a 7 or a 6 year old would need a nanny really. I'd get them to the local snow centre or dry slope before you go and that way you can ski with them in the afternoon too as they could cope with a nice blue.
To give you some idea of our 'no nanny' day. Ski 9 - 12 (or 9-1 if possible) in lessons.
Lunch 12- 1.30
Ski 1.30 - 3
break
3.30 - 4.30 (but my eldest by 6 would last later at Easter)
Not the full first lift/last lift of my child free days, but not bad.
In Canada the kids are in lessons 9 - 3.30, my 5 year old was fine.
I'm slightly ski obsessed so I suppose I've pushed our kids to ski, but skiing together and enjoying the slopes in the afternoon has been the highlight of my holidays. I never thought a gentle afternoon could be so much fun, but my husband loves it too. The 7 and 6 year olds will love (I would hope) doing little jumps off the side, skiing backwards, doing 360's. Practicing proper carving techniques, little bumps, it's endless and really good for your own skills too. I'd not send them home.
My DDs could ski pretty well by 4 so you may find the smaller ones will stay out a couple of afternoons too. I think they do get tired and also it's frustrating for them when they can't keep up. An extra hour on the nursery slope then home with the nanny is definitely doable.
The only child I have no ski ambition for is the baby 
.
As I said, I'm ski obsessed, but honestly, the older kids will surprise you at how good they can be. Definitely worth getting to the dry slope first if you can though.
goes off to look at ski porn