Please guide me on this itinerary

Can’t speak to the Italy portion, but if it were me, I’d remove st moritz and Engelberg, and do three nights Luzern, and four nights Murren. Or do two nights Luzern, five nights Murren.

I agree with David although I'd make Luzern your last town. Unless you have an early flight, you can stay in Luzern the night before a zurich flight.

Thanks David and Jules.

We want to do Bernina express train from tirano to St Moritz, that's why have planned the longer route from lake como to St moritz to luzern?

If we don't do bernina express and take other train, we can get from Lake como to Luzern in around 4 hours. Bernina express route takes 8+ hours.

Is it worth it to fit in bernina express in schedule?

I'm a bit confused- do two days mean three nights? It's more functional to schedule in terms of where you're sleeping.

This is a lot of moving about, and assumes your teenagers are morning bodies and can get up and out early day after day, with little break from the hectic routine. IMHO, you need to slow down, take a day off to perhaps nurse a cold, do laundry, adjust for weather, and/ or do nothing.
Also, your transitions will be much more than four hours, once you include hotel checkout , getting to the train station early, finding your correct tracks , actual train travel, delayed trains (Italy, not Swiss), getting oriented to the new destination, finding the hotel, checking in, etc. Then there's taking time to actually eat.
I agree, delete Engelberg , more nights in Murren, and put Lucerne at the end, from which you can commute directly to the Zurich airport. It's disappointing to have so little time in Venice and Lake Como.
What are your teens interests ?
Do you already have lodging secured? Some of these areas book up 6 months in advance. Are flights booked? I'd almost suggest skipping Rome and flying into Venice or Milan.
You've done a lot of research, based on your earlier post and revised itinerary. However, I do feel you need fewer transitions. Have fun planning.

Also, whether to do an 8 hour train ride is a personal preference. I love trains, but that’s like 5-6 hours too long for me.

Agree w/ everything the above posters said. Also forgot to mention that if you don’t have your hotel
Booked yet for mid-July in Murren, you might have a hard time!

Thanks Pat for very helpful inputs.

My air tickets and hotels are booked. But I see AirBnB avaialbility in rome and venice, so I can switch around hotels little bit. My boys want to see Rome, we want to see Venice. Lake como is optional.

We all are interested in enjoying hikes and nature in switzerland. We plan to do some hikes in lauterbrunnen valley, Jungfrau and Lucerne city, Mout Pilatus, interlaken and Rheinfalls.

Shoudl I skip St Moritz and do 3 days in Luzern?
2 days Murren?
and last nights Zurich? Zurich hotels or airbnb are available, but nothing in luzern and murren at this point in time.
Is Bernina express worth it?

I have Hotel Alpina in Murren booked for 2 days in July, Engelberg Airbnb booked for 2 days. I have Ibis hotel booked in Luzern for 3 days, but was planning to change to 2 days, so I can do Bernina express and break my 8 hour journey in St Moritz(after 4 hours) and then head to Luzern( 4 more hours) next day.

By two days you mean two nights? Which is one full day.

Yes, 2 nights.

Any inputs on my itinerary? In the last stage of planning all the details.

Please advise on Bernina express? Is it worth it? How can I optimize the trip? And what should I drop?

I think folks have answered that for you…

Again, much is personal preference. Most people seeking the outdoors and natural beauty would likely prioritize Murren over those other places.

My personal advise is that you're trying to cram way too much in. You're going to see more of the inside of a train than you will anywhere you're actually going. You've left no buffer for poor weather in the mountains or time to relax and enjoy the places you're in without constantly packing up and moving. For 12 nights I'd recommend 3-5 bases max. Since you already have your flights, I'd recommend removing atleast 1 spot in Italy and 1 spot in Switzerland. I'd probably remove Lake Como (you'll see a lake in Luzern) and then decide if you want to prioritize the Bernina Express, because it's going to add complication to your plan.

Maybe something like...
3 nights Rome
2 nights Venice OR Lake Como
3-4 nights Luzern OR Engelberg (it's less than 1 hour to do a day trip to Engelberg from Luzern, so really no need to stay in both, pick one -- Engelberg will be less touristy if that's of interest to youI
3-4 nights Murren, Wengen or Grindelwald, depending on where you can find lodging this late

Spend as much time in Murren/Wengen/Gimmewald as you can. Well worth the time spent

Thanks so much everyone for all the feedback. It really helped me plan out the details.

I am skipping Como. In switzerland, I am not finding many lodging options at popular locations at this point in time. I am skipping Engelberg and instead going to bern for last 2 days as it is more central and has more options on things to do. I am skipping bernina express, as it was making the itinerary complex. Instead I chose other panoramic trains to enjoy the experience.

18-Jul Rome Flight: 14 hr 45 min Checkin
19-Jul Rome Morning: Vatican City, Evening: colosseum
20-Jul Rome Trevi fountain, Pantatheon, Roman Forum, Spanish Steps
21-Jul Venice Rome -Venice 4 hrs train, Checkin hotel, Ferry to Burrano, Murano island
22-Jul Venice Gondola ride, rialto bridge, St peter basilca
23-Jul Luzern Venice - Luzern 7 hrs train, Route: Venice to Arth Goldau, Goldau to Luzern (Scenic Gotthard route), Checkin
24-Jul Luzern Lake lucerne boat tour and Mt Pilatus in morning, Go to Rheinfalls in evening
25-Jul Luzern Train to Stans and do the Stanserhorn hike
26-Jul Murren Luzern-Murren 3 hrs 15 min,Luzern Interlaken express(Panoramic train), Checkin, North face trail and Scilthorn
27-Jul Murren Jungfrau + Grindelwald + first cliff. Take eiger express to grindelwald and then first cable car to do the thrill walk
28-Jul Bern Murren to bern 2 hrs train, Route: Lauterbrunnen to Interlaken, Interlaken to Bern using goldenpass express via spiez(Panoramic train). Sit on the right side to get beautiful views of lake thun. Spiez is a wonderful little town on shores of lake thun. Finish up pending things in Murren(trummelbach falls, Panorama trail in morning) then take train to Bern. Checkin
29-Jul Bern Glacier 3000, Saanen bridge, Chillon Castle, Walk through prettry town of Spiez with its vineyards, Spiez Castle(pick few things from the list)
30-Jul Zurich Train (1 hr) + flight (11 hrs),Bern to Zurich(1 hr train), Zurich to LAX flight (11 hrs)

Let me know if you have any other inputs. Also, please guide me on which swiss pass should I take based on my itinerary? Half fare or swiss pass ?