Hi Tracy -
Here are some thoughts for travel to the destinations you have listed exactly as in your proposed itinerary.
Day 3 -
Momtreux to Interlaken via the Golden Pass Route.
Golden Pass Route and Trains:
The link notes that there are three sections of the Golden Pass Route.
The trains that travel those routes may be regular trains, or, apparently , some different varieties of Golden Pass Trains. i do not understand the differnces between "Golden Pass" "Golden Pass Classic" and "Golden Pass Panoramic." I note that GP Panoramic has VIP seats. I think this is a special car up front with especially good viewing. Any train on those routes will give you excellent views, even if they do not have panoramic windows. The best part is the route from Montreux to Zweisimmen.
This link may give added details:
As far as i can tell, the trains on the part from Interlaken to Luzern are now called "Luzern-Interlaken Express" rather than "Golden Pass"
I looked up travel times in the timetable on a random day in July 2016, specifically 22.07.2015, a Friday.
In order to prevent the computer from selecting the alternate faster routes - default is fastest - I had to enter "Zweisimmen" in the "connection" or "via" box in the screen.
I have attached a screen grab showing information about some of the morning trains from Montreux to IO (Interlaken Ost.). You will find the timetable helpful as you explore these options. If you open all of the journeys through Zweisimmen, you will find times of abot 3 hours to about 4 hours. Some have one change at Zweisimmen; other also have a change at Spiez.
Interlaken is not much of a tourist destination. It is a transfer point between the mountain railways and the main line trains. To appreciate the area, it is most desirable to continue southward from IO to - for example - Grindelwald, Wengen, Kleine Scheidegg or Mürren. That will consume from about 90 minutes to a few hours for various round trips. Spectacular scenery.
www.myswissalps.com/berneseoberland and www.myswissalps.com/jungfrauregion
A forum member who visits the region frequently has written a thorough discussion of Wengen and nearby attractions:
Other routes - Interlaken to Montreux (or the reverse direction.)
In addition to the Golden Pass route through Zweisimmen, there are three other reasonable and fairly direct routes between Montreux and Interlaken.
One is very scenic and takes on the order of 3 /12 hours, similar to the Golden Pass Route. It is the route through the older Lötschberg Tunnel then down the "Südrampe" (South Ramp) along the wall of the Rhone Valley down to Brig and thence west and north along the valley to Montreux.
In another post, I'll put up some photos of the Rhone Valley and of thehiking trail which parallels the train line as it descends into the Rhone Valley.
Kandersteg is the mid-route choice to insert in the timetable, and also the entrance to the older Lötschberg Tunnel in the southbound direction.
The other two are substantially faster. In the range of 2 1/4 hours plus/minus
One faster route also goes to the Rhone Valley, to Visp or Brig, and then follows the valley to Montreux. However, it uses a new lower, longer faster tunnel, and thus bypasses one of the most scenic train rides in Switzerland that you could see on the older route. .
The second fast route is from IO to Bern to Lausanne to Montreux.
Both of these faster routes will be shown on the timetable, without needing to enter a "via" station because they take about the same time and are the fastest. You can force them through Bern, or leave the mid point empty to get both routes.
I have attached screen grabs for the faster routes and for the older scenic Lötschberg route.
You may consider a faster route for your return on day 3, to give more time in the region south of Interlaken.
You will take any one of the four routes described above to IO, then to Brienz, which is just a stop or two beyond IO in the direction of Meiringen and thence Luzern.
The trip up and down the Brienzer Rothorn takes a minimum of approximately two hours + time to walk around up there or eat or both.
Day 7 - Luzern-
Two ways to go - via IO or via Bern
Via IO - To go to Luzern you can take any of the four routes noted above to IO, then continue via Meringen to Luzern. the route through the Brünig pass is very scenic...especially on the descent to Luzern. I like it better in the return direction, personally. That trip takes 1 hour 51 minutes and runs once per hour. Some or all trains may have large window cars. It also is or used to be called part of the Golden Pass Route.
Via Bern to Luzern -
Substantially faster on the route Montreux to Lausanne to Bern to Luzern -
This repeats part of one of the fast routes from Montreux to IO, but, in Bern, you continue to Luzern rather than to IO.
The trip takes 2 hrs 37 minutes at xx23 with change only at Lausanne, or or about 3 hours with other connections, typically through Olten. The most scenic part of the route is from Montreux to Lausanne, but the rest is pleasant.
These data should give you some ideas for planning the days of those trips.