Just did some calculating and found the following prices, second class and per person:
Zürich Airport – Sion CHF 94 (return ticket CHF 188)
Sion – Crans Montana CHF 18 (single ticket, twice))
Crans Montana – Lugano CHF 181,60 (return ticket) Please note that reservations may be needed, you can ask the Railway personnel in Crans Montana. This will cost a bit extra.
Crans Montana – Lausanne CHF 89,60 (return ticket)
Crans Montana – Jungfraujoch CHF 296,80 (return ticket)
As you see I calculated every trip you mentioned from Crans Montana as you have a hotel booked there.
Total costs: CHF 792. This, times two will bring you to almost CHF 1600
A Swiss Saver Pass (for 2 persons travelling together) will cost you, for fifteen days: CHF 387 a person
This Pass will give you a discount of 25% to Jungfraujoch – you can travel for free to Wengen or Grindelwald.
Return ticket from Wengen to Jungfraujoch: CHF 149, with discount CHF 111,75
Return ticket from Grindelwald to Jungfraujoch CHF 162, with discount CHF 121,50
In your case I would opt for a Swiss Saver Pass, which you can order online
. If you don't have time for ordering online, you can purchase your Pass at Zürich Airport Railway Station. Your child will travel for free.
I don't know if it's cheaper to buy your Pass in Singapore, but I suppose not, though I'm not quite sure.
Wishing you a very pleasant stay in beautiful Switzerland,