<<"as would I but time is of the essence as we are meeting up in Montreux
with my daughter husband and 2 babies!!! (Aged 1 year and 3 months) who
are flying into Zurich from Australia and we've organised an apartment
on the Grand Rue for 4 nights. How do think Montreaux will go as a base
with young children in tow??">>
You've picked Flixbus, so that the earliest you could get to Gare routière in Geneva is 1205, assuming that the current schedules hold for next year.
Allow 20 minutes to get to Cornavin if you have luggage.
The earliest you could get to Montreux is 1337 if you caught the direct train at 1230. Possible. Next chance 1242 change in Lausanne, arrive at 1402.
Next chance 1300, no change, arrive at 1410.
Don't know when your relatives arrive from Down Under, , but the fastest trips to Montreux are trains at xx18, xx40, and xx43. All require at least one change. With good luck and fast kids ( unlikely, I'd guess) your relatives might be on a train 45 minutes after their plane gets to the gate.
So, count oun somethng close to 4 hours fro them to get to Montreux.
Not sure how those timesmatch up, but I assume that you want to be in Montreux whe they arrive.
Considering the nature of the towns, I think they'd enjoy Luzern just as much as Montreux. Luzern has a beautiful lake, and more relatively level land for walking. The older child might appreciate the Lion of Luzern. My much older grandaughter ( then 8 years old) was fascinated. See attached page from a photobook that I prepared documenting her trip in 2009.
There are more varieties of lake boat rides. Luzern is about 1 hour from Zürich Airport. Trains take either 2 minutes or 7 minutes more than one hour. The faster ones, with no change of train , leave at xx18. The slower ones, with a change at Zürich main station, leave at xx47.
A shorter train ride might be appreciated after the flight from Australia.
If you use the same , earliest, Flixbus frm Annecy to Geneva Gare routiere, you would only reach Luzern from Geneva by 1555 (depart Geneva main station at 1242 with 2 changes) or by 1600 (depart Geneva Cornavin at 1312 with no changes.
However, if you chose the slower but earlier T72 bus to the airport, easing luggage transfer, you could arrive at the aeroport by a bus ride that is 50 minutes longer than the Flixbus, at 0540, 0747, 0815, 0840, 0949, 1030, 1144......
If you took the not-so-early 7 AM departure from Annecy, you'd be atthe aeropoert at 0840, and have time to catch the 0902 direct to Luzern ( no changes) . You would arrive in Luzern at 1200. Those trips generally take about 3 hours with various possible connections and timing.
You could consider buses from Annecy that are as much as 2 1/2 hours earlier. allowing you to reach Luzern by 0905 with an easy change at Olten.
The object of this exercise in using the schedules and timetables is to let you deal with your point that "time is of the essence" and and also answer <<"How do think Montreaux will go as a base
with young children in tow??"">>
It lets you bear the brunt of the longer train ride and early departure from Annecy, and in turn, allow your relatives the shorter, easier journey after their flight.
Of course, I don't know what time of day they will arrive. Nor whether the children will be manageable on a 3-4 hour time between the arrival at Zürich on the plane from Australia, and arrival at Montreux. (Note the spelling.)
But, I think Luzern is a good trade off for or perhaps even better than Montreux, with the constraints you have outlined. That is my response to your question -
<<"How do think Montreaux will go as a base with young children in tow??"">>
The most decisive element in your plan is whether or not you choose to take the fast but not early Flixbus to save a few Euros and then make the afternoon short trip to Montreux, or, get to either town much earlier , by using the slower but earlier and more frequent bus service to the Geneva aeroport.