Karlsson, the Relais de Glaciers is the one that matches your brief.
If you drop the swimming pool, then I'd suggest La Rouja or Hotel de Champoluc.
If money is no object, stay at the Breithorn.
I've not stayed in the Mascognaz, it looks pretty impressive. My normal spot is the Rascard Frantze, but it doesn't have a pool and as far as I know it's fully booked for next year.
In terms of getting there, I've travelled with Ski2 ( http://ski-2.com/
), Echo Travel ( http://www.echotravel.co.uk/
) and independently.
I can recommend both companies. My last trip was with Ski-2, they picked us up by car at Milan Malpensa (Turin is closer, but we booked too late to get flights there), then drove us up to La Rouja. It's a 5 minute walk from the lifts, but they have a ski/boot room there, so you walk up in your shoes, change to your boots, then hit the slopes. Ski-2 will also pick you up and take you to Frachey if you want to start your day there. As part of their deal you get lunch vouchers which you can use at several restaurants on the hill, or put them towards drinks in some of the bars. They also have their own instructors & hire shop.
Echo Travel is smaller, but also provides a very good service. (it's been a few years since I used them, so I can't remember all the details)