>> Will Mt. Pilatus or Mt. Rigi be possible options if we miss Mt.Titlis. Could they possibly have a weather different from Mt. Titlis?
As Lucas mentioned, if it's just a matter of cloud cover on Titlis, Pilatus or the Rigi might not have the same cloud cover. If it's more a question of stormy and rainy weather, I suspect it would be pretty much the same at each location.
You can check the weather and webcams on the respective websites for each mountain:
>> Is the Glacier Express a viable option from Luzerne.? We have a Swiss Pass. And would prefer to do part of the ride . Not the complete ride . If so which is the best part of the route.
Not really. Reservations are compulsory on the Glacier Express. If you are wanting to travel on it at short notice, chances of getting a reservation are pretty remote I would think.
You could travel along part of the route on normal trains. If you wanted to do this, I would suggest the route Luzern-Erstfeld-Göschenen-Andermatt-Sedrun, which takes in the rugged Schöllenen Gorge between Göschenen and Andermatt, and then goes over the Oberalppass (which is one of my favourite parts of the Glacier Express route).
That would take 3 hours each way, and you would need to come back the same way. The reason I suggest going as far as Sedrun is because there is a nice restaurant at the station, where you could have lunch before heading back to Luzern.
There is always a chance that clouds could spoil this trip as well. I did it one day because it was a very wet day and Titlis, Pilatus and the Rigi were in the clouds. Whilst there was a lot of cloud around, views along the Glacier Express route were still wonderful, as the clouds were moving constantly. However, visibility at the Schöllenen Gorge was very poor, as was the view over Andermatt, which was completely obscured by clouds.
>> Museums I believe are closed on Mondays. 19th is Monday.
Some are. The Swiss Museum of Transport, the Rosengart Collection and the Bourbaki Panorama are open on Mondays.
>> Alternatively could we then go to Rhine falls or Zurich tour even in rainy weather?
Well, the Rhine Falls is an outdoor attraction, so you would want to check the weather there.
Walking through Zürich old town would be nice, and there are plenty of cafes to take refuge in if the weather is unpleasant, but if you have not by this stage walked through Luzern old town, in my opinion that would be a better option than travelling all the way to Zürich.