PalenQ

That is a long expensive train ride if just to see the Matterhorn and rain can materialize so so quickly - even fog or cloudy weather can often obscure the Matterhorn - I'd say train fare may be $100 or so each way plus more if you want to take the mountain train to Matterhorn's icy top.

But train goes like this - Lucerne to Bern - Bern to Visp - Visp to Zermatt - 3 hr 15 minutes each way or about 7 hours on train there and back - I think Mt Titlis will more than fulfill your idea of an Alpine Wonderland.

The Rhine Falls near Schlaffhausen makes a neat day trip too - even in wet weather - probably less than 2 hours from Lucerne - take trains right to the falls - Schlaffhausen is also a very neat city.

Don't neglect Bern - to me a wonderful city - they also have covered walkways in case of rain in the town center - check out the Bear Pits overlooking the rushing Aare river - rent a kayak and do a little boat ride. Bern is special and makes a nice short day trip from Lucerne.

PalenQ

Wednesday we may take train to Zermatt/ Matterhorn area, someone told it isn't raining there>

you can easily check weather cams before setting out - most hotels I've been inin Switzerland have them.