It s a real pity you already bought tickets from Wengen to Basel, and via OMIO no less. OMIO is just a travel agent. There is normally no need to buy trains tickets in advance in Switzerland.
Best to get for you is the Half Fare Card. That comes with the free family card, which means your children go everywhere for free.
With that your trip up the Jungfraujoch goes from 500,- to 100,-...
Currently getting to Wengen from Milano is a bit complicated however. Trains will be partly substituted by busses on your route. However the trip is doable. Or are you perhaps starting out at Milan Airport and not going in to the city? That would change things.
So your shopping list is:
- Get the Swiss Half Fare Card. 120,- CHF
https://www.swissrailways.com/en
(This is an official website run by the Swiss Railways, so a good source).
- Get a ticket for you and your children for Milano - Domodossola (Italian - Swiss border) on www.trenitalia.com book one of the "ECxxx" busses. Ticket should cost you 31,50 Euro.
(If coming from the airport book a bus from the Airport to Domodossola here: https://www.comazzialibus.com/ComazziAlibus/?locale=EN)
- Get a ticket for your self at half price for Domodossola - Wengen. Once in Switzerland your kids no longer need a ticket. Buy on www.sbb.ch, cost for a normal ticket 37,-, there may be discounted tickets. Try to plan min, 15 minutes between the arrivial of your bus and your train. However, if the bus is delayed and you miss your train you just take the next one. Even with a discounted ticket.
Buy tickets for excursions locally on the day of travel.
Now it is a pity that you already bought tickets to Basel. You can buy a ticket Wengen - Basel Airport for CHF 42,80 on www.sbb.ch. That again is assuming you have the Half Fare Card and the Family Card, so your kids go free. That ticket includes the bus to the airport. General rule in Switzerland: One Trip, one ticket, no matter how many trains, busses and other vehicles are involved.
So if you can get a full refund from OMIO. They probably sold you a standard ticket, which should be completely refundable.