Don’t worry about travel too much - it’s just the first and last bit of the holiday. It’s the bit in the middle you really want to think about. I would be avoiding Scotland - as you say, not too far but not set up for young families. Europe is absolutely stuffed full of companies that specialise in family snow holidays, and resorts and hotels that offer childcare so both parents can ski together.
We had lots of happy holidays with Ski Famille in France. We stayed in Les Gets with them, but have heard from friends they are as good in other resorts. They provide childcare, the chalets are nice, and the resorts are always very family friendly. Les Gets is very villagey, with main shopping street, ice rink. Avoriaz is just up the hill and is very snowy - no roads, just horse drawn sleighs and snow bobs for transport, it has a family swimming complex.
We also stayed with Ski Esprit in Italy - again fab holiday but less polished in their child care, even though that is what they specialise in.
We stayed in a Kinderhotel in Austria, which MN rave about, but we’re kicked out with nowhere to go when my son developed chickenpox. The concept is fab, but I would not touch Kinderhotel with a barge pole after our experience. However Austria again do family snow holidays very well, and any ski resort you look at will have a ‘familienhotel’ or two designed to make families with children easier. We’ve been in Saalbach the last few years and although it has a bit of a reputation as a lads’ resort it also has a lot of family accommodation too. Austria has a lot of family resorts.
i have a relative who only ever holidays in scandi, but my experience is that it is flupping freezing and a bit basic out there (they self cater and take grandparents with them for childcare) but is definitely snowy!
if you can be more specific about what you want (is the travel, accommodation, facilities, snow, food, or what most important to you?) I could happily waffle on about snow holidays all day.
for now though, you can’t go wrong with Ski Famille.