TD,
Zürich is probably the easiest place for an intermediate stop as you'll likely have to go through there on the way to Salzburg anyway. It's a large and expensive city, but with only one night there the costs should be manageable.
Travel from Mürren to Zürich will be about 3 hours, depending on which train you choose. Since there's no hurry, you could enjoy a leisurely breakfast in your hotel in Mürren and then be in Zürich in time for a late lunch. For the trip to Salzburg, there appears to be a direct departure via RailJet at 10:40, arriving 16:03 (time 5H:23M), which would be the easiest solution. I'd probably pack a lunch (although there should be a dining car on the train). There are lots of food vendors in the Zürich station.
One suggestion for accommodations in Zürich is Hotel Walhalla. I found it to be very modern and comfortable, and it's only about a 5 minute walk from there to the rail station. There's a Tram stop right outside the door, and also some of the local tour buses depart from the bus terminal 'SIHLQUAI' right across from the hotel. THIS tour is one example. It's a very convenient location!
I'm a bit reluctant to mention this, but if the kids are in the mood for a "taste of home", there's a stairway leading to the underground Rail City about a one minute walk from the hotel front door, and there's a Burger King at the bottom of the stairs.