We arrive in Zurich on April 6; Go to Luzern for 2 nights; Go to Murren 3 nights. Then we go to Lugano for 1 night before finishing in Varenna for RS 17 Day Italy tour. I am having difficulty determining the best route from Murren to Lugano. Should I return to Luzern and then head south or go towards Brig and around?
According to the rail websites, one of the quickest trips will be a departure from Mürren at 07:06, arriving Lugano at 12:26 (time 5H:20M 5H:20M, 4 changes. The aspect of four changes may seem onerous but in this case they're all very easy. Arriving at that time will allow time for a nice lunch and exploring the town.
Since you'll only have one night in Lugano, it would be prudent to minimize travel times to allow as much time for sightseeing as possible. The trip from Lugano to Varenna is relatively easy.
Yes, back to Luzern is the quickest way.
The route through Brig/Domodossola is great in the sense it covers the scenic Centovalli railway. It does take longer, however.
That is a viable way to go and can be done in the same or less time than the route through Luzern, but instead of 4 to 5 train changes through Luzern, you will have 7 to 8 changes using the Centovalli route. Of course, it takes 2 changes just to get from Muerren to Interlaken Ost regardless of the route you take from there.