What dates in May are you in Switzerland, at what city will you arrive, and from what city will you leave? Times of day for arrival and departure are helpful, too. For us to suggest an itinerary, it is helpful to know where you are starting and where you are finishing, and whether you might have some time on arrival or departure days to do something. ;-)
Also- any spcial interests...hiking? Cities? Countryside? Museums? Anything special for the kids? There are some very nice playgrounds in Switzerland, including a large one by the lake near the Transport Museum in Luzern, and others here and there. My 8 year old granddaughter loved the one at Männlichen near the Jungfrau. May still be snowed in in May. Altitude approx. 2300 meters.
At lower altitudes, May can be quite nice. Spring is well advanced.
May is a good time to visit, except in the high Alps. At higher altitudes near the Jungfrau, the snow is pretty well gone for skiers, the trails are either snowy, icy or muddy, and the summer season really doesn't start up until about June 15th. So, while some very nice things are available, especially at the lower altitude areas, a lot of cableways and hotels are shut down for between-seasons break. June would be better. However, it is till definitely worth some time to be in the Jungfrau region. That said, Luzern will probably be a better base. That is not definite, and Interlaken might fit the full set of travel routings better, but Luzern seems more likely.
The Golden Pass route includes a section running between Interlaken and Luzern, except that particular section of the Golden Pass route route seems to have been renamed as the Luzern - Interlaken Express.
With either base (Luzern or Interlaken) you'll have some long travel days if you choose do all the things you stated. (By the way, it is Stanserhorn not Staserhorn, not far from Luzern.)
For a trip of that length (about a week) many people find two bases to be helpful, to reduce the amount of time on trains. However, it is not necessary or critical. Luzern and Interlaken both are reasonably centrally located. You can see a lot in one week using either one as a base. And, you can't see all of Switzerland in one week,anyway. ;-)
Here are some links to help you out:
Very important -
If you use the forum search feature, you can look up Titlis, Jungfraujoch, Matterhorn, and, maybe Stanserhorn, as well as other places of interest. It works quite well.
Some time with those links will help answer your questions, and, surely, generate more questions. They might be enough for you to rough out an itinerary on your own, for the forum members to help you refine it.
Once you have an itinerary, then rail passes can be considered.