I am late to the conversation; I just saw this discussion this morning. Reading the responses I got as far as this statement before I felt the need to add my voice:
It is near the end of our trip and I was simply thinking we would be done with trains and it could be fun to do a scenic trip down the coast of Italy.
I was in a car with 3 college friends driving the coastal route to go between Rome and Florence in the winter 50 years ago (I was not the actual driver, I was in the back seat). I do not recall every bit, but I do remember visiting the Carrara marble quarry, and the little hotel in Portofino where we spent the night. I do not remember the scenery at all because from La Spezia north to Portofino the road is mostly in tunnels. I still have my diary with the entry about that road and the “endless mole tunnels”.
I would be surprised if they have somehow managed to build a tunnel-free road along there. So I am glad to see you have changed your mind about the car.
To address your question about which train route to take from Lauterbrunnen, I will note that the first step will be to get yourselves from there to Milan. The “usual” route goes via Spiez and Domodossola, but that route will be affected by a track closure between Stresa and Arona. There should be a bus connection around the closure, but those have not been put on the schedule yet. So if you look at that part of the journey now, you will see that the Spiez route goes as far as Domodossola, then from there to Locarno with the Centovalli railway, and thence to Milan. Or you can choose the other direction, via Luzern and the Gotthard Pass route to Bellinzona and then to Milan.
As for the routes from Milan to Manarola, as you have seen there are two options, the inland route via Florence andLa Spezia, and the coastal route via Genoa and Levanto or Monterosso (where you pick up the regional train to Manarola). In general, the Florence route is slightly faster and may have more connections, but it all depends on what time you start in Milan.
We prefer to minimize the number of train changes, so when we took our daughters to Italy 14 years ago, with a stay in Manarola, we chose the coastal route to return to Milan. We took an InterCity train that connected Milan with Monterosso without a change at Genoa, taking just about 3 hours. That train runs several times a day; the ones that might be useful to you would be IC 665 departing Milan at 12:10, and IC 669 departing at 14:05.
However, I also see a direct train to La Spezia, FrecciaBianca 8619, departing Milan at 13:10 and arriving at La Spezia in 3 hours.
Both the IC and the Frecce trains go along the coast from Genoa south (and there will be some tunnels). But there may be a difference in the type of train used, and since you are interested in AC you should find out more about that. The IC train we rode 14 years ago was the old style, with 6-person compartments and a corridor down one side. We were in First Class, but it wasn’t all that great as far as comfort, and the small compartment was “stuffy”. If they are still using that type of train on the IC routes, I would definitely choose the FrecciaBianca train instead. Economy tickets are available on Trenitalia now for July 15 for 29,90 in First (SuperEconomy tix already sold out).