Searched this website for views on Norway ans skiing, weren't many, but what is there is not all good reading.
snowheads.com/ski-forum/viewtopic.php?p=1343023&highlight=norway#1343023
Norway is not known as a downhill ski destination, probably the reason why no-one here can help you.
If you are complete beginners, really a package holiday is going to be your easiest way into this highly addictive past time.
Catered chalets are very very popular with British families. But flight + transfer + catered chalet (you've got ski hire / lift pass / ski lessons on top which can double costs)usually comes in at no less than £500 per head for the cheapest weeks, so not cheap for a family - my limit for EVERYTHING is £300 so I've never experienced chalet holidays with the children, enjoyed it alot before the children arrived when I was paying for just myself. Self-catering can be hard or easy, depends on access to a supermarket / deli. From the UK to France, the cheapest you can really do it as a family is DIY package at £300 per head self-catering, but you have to really pick a cheap ski week, know which resorts do family ski lift passes and cheap ski school and cheap ski hire, you'd only achieve that price on a late deal through a package holiday. I'd really advise a package for flights/train-self-drive + accommodation, if you want to save money, price up lift passes, ski school, ski hire before committing to adding this to a package as I find only rarely can a hoiliday company offer this at less than buying direct from the resort. There are hundreds of cheap and not so well known French resorts, must be the case for Austria and Italy too.... you need to research well.
February is mega expensive in France, prices for accommodation can easily double, more importantly for beginners the slopes are at thei most crowded. Never skiied Austrian or Italy but guess is similar story there in February.
Consider the weeks around Christmas and next year the first UK schools Easter week when French schools are still in session. For Austria and Italy, you'd have to research when their holidays are.