Help with Swiss rail tickets - I'm confused

Hello Zandan, welcome to the forum! The regular costs per person and in 2nd class of the trips you mention, which can be calculated in the online timetable, are as follows:

- Zurich Airport - Lucerne: CHF 27.00
- Lucerne - Engelberg (base of Mt. Titlis) - Lucerne: CHF 32.00
- Engelberg - Mt. Titlis - Engelberg: CHF 82.00
- Lucerne - Zurich Airport: CHF 27.00
- Total: CHF 168.00

This doesn't include bus transportation and boat trips in and around Lucerne yet, as I'm not quite sure what trips you have in mind. Prices for the boat rides can be found at the website of Lake Lucerne. If you add the price for a boat trip (just to give an example: from Lucerne to Alpnachstad and back, which costs CHF 38.00 and would make a total of CHF 206.00) and urban transportation in Lucerne and Zurich, you're best off with a Swiss Half Fare Card. This offers a 50% discount on most trips, including urban transportation in Zurich and Lucerne. You would pay CHF 99.00 for the Swiss Half Fare Card and CHF 103.00 (for the example I just mentioned) for the other trips, which makes a total of CHF 202.00.

A 3 day Swiss Saver Flexi Pass costs CHF 212.00, but you should add the costs of a discounted return ticket Engelberg - Mt. Titlis to this. So in all, it's a more expensive solution than the Swiss Half Fare Card.
Your children travel along for free if you order a free STS Family Card along with your passes.

I hope it's clear now!