Hi Sandip
Even I’m concerned that @RolandP will give you a better advice, my opinion here underneeth 😉
I just calculed the price for just one persons from Lucerne to Rigi Kulm an from Lucerne to Interlaken. I came up with a total Price of CHF 96.60, without any other bus transportation or any other track that you will my experience that day, in the first option.
The price for a saver day pass for tomorrow (01.05.2024) is CHF 119. Having said that, you could then have a look two days in advance for the weather and see If you place your first or second option in act and then purchase (if there are some left - should be the case in my opinion) the saver day passes. I just checked now for tomorrow (01.05.2024) and there is availability.
Unfortunatelly in your case there isn’t a 1 Day Swiss Travel Pass or any other Passes for international clients, so far I know.
Please be aware to calculate the right times for your trip to Rigi, because from Lucerne to Interlaken it’s a trip of 1h and 49 minutes.
Depending how old your children are, be aware of these informations
Hope that I could help you.
BR
Romano