A normal ticket is available from about 50 € (dynamic prices) per person.

There's a pass that does cover most mountain railroads, boats, busses and gondolas in that area (except Schilthorn and Jungfraujoch) and covers the train from Luzern and the one to Brig on your way to Zermatt,; maybe have a look: https://www.berneroberlandpass.ch/

To go by train in Italy is cheap and these are short trips. So normal tickets might be cheaper.  

You do even need a valid travel day for the discount. 

Summary: I'd check normal ticket prices first before buying any pass. A combination of two rail passes will not save money most of the time. The regional pass linked may be  more interesting. The only expensive trip is the one from Visp to Zermatt and back.

I agree with Hektor : 2 passes won't make sense.

The Swiss Travel Pass is considered (too) expensive.

The Swiss Half-fare card (or the STP) would give you 50% on Gornergrat and/or Matterhorn Glacier Paradise. I assume you're likely to go there on 13th May.

You get "only" 25% discount on Jungfraujoch with Eurail and the STP. 50% with the half-fare card. 50 CHF difference.

You need to compare but I guess I'd take the Swiss Half-fare card (+ maybe the Berner Oberland Pass which has a discount with that card).

Munich - Zurich - Lucerne has cheap advance tickets (Sparschiene) : for example 69.90€ 1st class for the 08:54 departure on 8th May.

Don't worry if you miss the connection in Zurich (the EC is usually 30 min late) take the following train. :)

Note that you'll be travelling during 2 busy holiday weekends (Ascension and Whitsun) so you should book Munich - Lucerne and Domodossola - Milan (by Eurocity train) in advance for the best fares.

Point-to-point tickets in Switzerland and regional train tickets in Italy have a fixed price and cannot sell out so that's not an issue.

No you don't because that contradicts the pass’ conditions of use. If they make you pay anything extra or use a travel day, you should be able to get that refunded.

What is the age of the children?

For Eurail the age limit for children is 12 but for a pass from the Swiss Travel System the age limit for children is 16. This might affect the price you pay depending on the age of your children.