You will find it hard to get better views than what you get along the Chamonix valley. For non skiers looking for views and train / cable car / telecabine rides, you have the :
Tramway du Mont Blanc from St Gervais,
Train de Montenvers to the Mer de Glace from Chamonix which is a huge glacier you take a train to then a telecabine down to, with an ice cave full of sculptures,
Téléphérique de l'Aiguille du Midi from Chamonix, one of the highest cable cars in the world, you can go further over the top of the mountain into Italy,
Téléphérique des Grands Montets form Argentiere, another high cable car,
Télécabine de Brévent from Chamonix,
Télécabine de Vallorcine,
Téléphérique de Flégere from Les Praz,
You can do all these trips by buying a Mont Blanc Unlimited pass. If the children are less than 4 years old, a 3 day pass would set you back 292 euro. This might sound much but a return trip just on the Aiguille du Midi cable car for 2 adults is 91 euro. If you did 2 cable cars/train/télécabines per day, you could easily pay 400 euro plus for the individual trips for 2 adults.
There are reasonably cheap places to stay in the Chamonix valley with indoor pools, especially if you stay in one of the other villages in the valley other than Chamonix, such as Les Houches, Argentiere, Vallorcine. If you stay along the valley in paid accommodation between Servoz and Vallorcine, you get a free card for the local trains and buses too. You should be able to find a self catering apartment from 500 euro per week along the valley with a pool, less without a pool.
www.compagniedumontblanc.fr/pages/forfaits_tarifs_excursion_hiver.html