I, personally, would not stay in Zurich with a family. Lucerne is much nicer and offers a lot more for children, compared to Zurich. The latter is rather a banking city and not conveniently located for day trips to other parts of the country. Plus, Zurich is expensive, not matter what. If you do not have family there, consider a change of base.
The Saver Day Pass and the Children Day Pass is fully covering the Mt. Rigi visit, so does it also includes the boat ride from Lucerne to Vitznau. Make sure you will catch one of the paddle steamers, this will be great fun for the kids and unique in the world! The Museum of transport is also great fun and very interesting for kids.
For the kids, I recommend the Junior Card. It costs CHF 30.- per child and is valid for 1 year. With it, kids travel for free everywhere provided you as parents hold a valid ticket. It is available at the train station only.