Hi, I would recommend that you go to Banff, and ski mainly in Sunshine Village. They are very geared up to children and the blue runs are a lot more forgiving of novices that Lake Louise's blues.
There are plenty of inns to stay in Banff, and it is very laid back and great with kids. It is also a quicker ski bus to Sunshine, about 25 mins iirc. Also Banff is a proper little town, unlike Lake Louise, so you can do other things besides skiing if you want.
Also Sunshine Village has a ski in, ski our hotel at the foot of the slopes; have seen this advertised in Inghams and Crystal. You get a free lift pass if you stay there (well, you would have to, the hotel is at the top of the major gondola up to Sunshine) and they lay entertainment/kids clubs etc on. I imagine it is pretty remote at night, because when the gondola closes you can't get anywhere, but looks like a fun place to stay. And you would DEFINITELY be first on the slopes!
I stayed at a place in Banff called Caribou Lodge (through Inghams) and I can't fault it. Free (monster sized) breakfast as well.
We went first week in April and it was ideal, very warm, but the snow wasn't at all slushy. Skiing in a Tshirt was great fun! Howwver I have been told that it is incredibly bitter in January and to avoid going then.
Hope this helps!