In reply to Arcturus:
Multiple objectives, but the biggest plus of group lessons is that they get to ski with other kids, side benefit is that my wife and I get some time out together, we generally get the touring skis out and skin for a couple of hours. We did also find that their technique improved, I think that they are more willing to listen to instruction from a 'proper' teacher than their parents, although I suspect we say much the same thing.
Ideally we would like another family to ski with, but multiple attempts to co-ordinate dates with friends (or even get them skiing at all) have failed. Long term aim is that we can take the kids on touring holidays, but that's a few years off yet.