<<"And 1 last question which trip is longer Rigi or Pilatus (obviously depends on how much time we spend at the mountain but travelling time? )">>
Your question is best answered by working with the timetable linked in an earlier post. If you do that, then you can look at different departure times and different return times. And, in both cases, but, especially for the Rigi, if you decide to go back to Luzern, you can judge alternate routes ( via Vitznau and boat, via Weggis and boat, as well as the alternate for both of those two by bus to Küssnacht am Rigi and train to Luzern, or, as a third option, by descent to Arth Goldau and return to Luzern by train.
Not only transit time is needed, but what hour of the day the transit runs is needed for your planning, as well as connecting times in some cases, and the boats do not have as frequent a schedule as the trains.
However, one way transit times for example on May 28th are-
depart Luzern Bahnhofquai at 0812, boat to Vitznau, catch the connecting cograil to Rigi Kulm, arrive Rigi Kulm at 0947.
Other times are available.
Rigi Kulm to Luzern via Arth Goldau is 1 hour 37 minutes, leaving at 1104 and xx04 for some hours afterward.
The following time table shows that you can leave Luzern at 0838 by boat, beginning on 28 May and arrive at Pilatus Kulm via cograil at 1007. Earlier in May, the first service is at 0938.
Hope that helps