Switzerland and Italy trip for 2 Adults and 2 Child (14 and 15 yrs old) between 07 to 18 Jun 18

I have no insight to offer about the train passes, but your plan to travel from Rome to Pompeii and back on the 16th and then doing Rome to Amalfi ( Coast/town?) on the 17th and returning to Rome the same day borders on crazy.
You would be better off to stay overnight in Sorrento, rather than make 2 round trips on consecutive days.

Your series on one night stays looks exhausting. You might as well skip Venice as it looks like you will be doing little more than checking in/out of your hotel before moving on. It would be better to add a night to Rome, than the hit 'n run through Venice.

1) I would choose to stay in Murren instead of Gimmelwald. Gimmelwald is nice to visit for about an hour (and super easy from Murren) but lacks any infrastructure such as restaurants and super market for food.

2) Do not waste your time going from Luzern to Zurich Airport to fly to Venice. The train from Luzerne -> Venezia S. Lucia is only 6hr 22min and is SOOOOO much more enjoyable than flying. The train will drop you right into Venice where you'll catch the vaporetto or water taxi to your hotel. If you fly you'll have to spend more time/money just to get into Venice from the airport.

3) spend more time in Venice than just 1 night.

4) Have you read reviews of Resort Roma Termini? They are bad: https://www.tripadvisor.com/Hotel_Review-g187791-d6916128-Reviews-Roma_Resort_Termini-Rome_Lazio.html

5) do NOT waste your time in Rome by traveling to Pompei and then another whole day to Amalfi coast. That's a REALLY bad idea. There's plenty to see in Rome.

6) Do NOT waste your money on Eurail passes.

7) Half Fare card will save you the most money. But Swiss Travel Pass will give you savings AND save time. Your children only need the free Swiss Family Card which you can get in the Zurich Airport at the SBB Ticket Counter.

8) No pass needed for Italy. Point to point tickets are cheap especially if you purchase them early. Purchase either from www.trenitalia.com or from trainline.eu

You can get a Family Card for your children for free with either a Half Fare Card or Swiss Travel Pass for the parents. The children will then ride for free on trains, lifts, and boats, including up the Jungfrau.

No pass needed for Italy. But tickets in advance on the fast trains (Frecce) for best prices. There may be family deals as well, but the Super Economy prices usually beat the family deals if they are still available.

Totally agree with Tim about taking the train from Luzern to Venice over flying.

I agree with what Tim has to say, and I also want to say that Murren would be better than Gimmelwald.

Gimmelwald is great IF you are a senior who wants a peaceful respite from the rat race, or a well-recognized travel writer who would like a bit of privacy. BUT it is not a great place for 2 teens!

I took my teens to this region and we hiked and explored every day. They loved it so much they've come back twice with me as adults to do the exact same thing. I'll list some hikes at the end.

Relatedly, you do not want to "sight see around Interlaken". Interlaken is nice, but Murren is fantastic.
Also, if you are going to Schilthorn/Piz Gloria (which is right up from Murren) then I wouldn't use up another day to do something very similar. Whereas Schilthorn can be done in a few hours, Jungfrau will use up basically a whole day.

Also at the Murren cable car station you can see the top on the TV monitor and decide if it's too cloudy or not. Not so easy with Jungfrau, where you spend most of your day on a slow train going up only to find at the end that you are in the clouds. Plus, teens spend enough time sitting around "watching things". Get everyone out exploring instead!
Here are several hikes in the area:

The first goes from Grutschalp to Murren. In your case, you want to hike Toward the mountains, so you should take the train to Grutschalp and hike back. From Murren, you can hike uphill on a diagonal from the Murren cablecar station, and eventually end up at the restaurant at Spielbodenalp. There you can get a drink and sit at a picnic table and watch the
cows. You can also get to Spielbodenalp via the Sprutz Falls route. About a third of the way up the trail branches near a hut. Take the upper one, you go to Spielbodenalp. The lower one goes fairly level into the woods and eventually to Sprutz Falls, which you cross under, climb up the trail on the opposite side, and end up in Spielbodenalp. You can see that trail and others here:

http://www.gimmelwald.com/pics/gimmelwald/hikemap.jpg

Also see
http://ontheworldmap.com/switzerland/ski/jungfrau/jungfrau-summer-map.jpg

Closer views in the Murren brochure here:
http://bro.jungfrauregion.info/Mue/Image/files/downloads/Gesamtbroschuere-Muerren-Gimmelwald-blaetterbar.pdf

Another goes from Mannlichen to Kleine Scheidegg. The walk itself is
about 2 hours, and we save this for the sunniest day, because of the panoramic
views. (Leave in the morning--most afternoons the peaks cloud up!) Take the
train from Lauterbrunnen to Wengen, then a 5 min walk to the cable car
station, where you take the cable car up to Mannlichen. Once up, you can look
left at a 30 min up and back trail to a lookout point. If you look right
there is the main trail that leads toward the Jungfrau mountain, which takes
1.5 hrs and you end up in Kleine Scheidegg, where you can catch a train down
to Wengen and finally Lauterbrunnen. Great panoramic views all along the
route. (Google image "Mannlichen" to see why.) This trail is so easy you could do it in a wheelchair.
It takes about 20 min train from Lauterbrunnen to Wengen, another 20 min cable car to Mannlichen, 1 and 1/2 hr hike to Kleine Scheidegg, 40 min train down to Lauterbrunnen.

Another great trail is to take the funicular from Murren up to Allmendhubel. Pet the cows there. Take the trail to the left down to Sonnenberg then Suppenalp then Schiltalp (cheese-making there), down the Spielbodenalp, then back to Murren.

Wished I had seen this post sooner and hope you get to read this. There are three very beautiful cities you plan to visit. I have been to Italy a number of times. At the least .... Two days in Venice is much more sensible. Florence is wonderful. So much to see there. I've been to Rome maybe four times in the past 10 years and to see this lovely city takes time. I have a good friend that lives there and it still takes days to explore this city. It would be next to impossible to add the Amalfi coast and Pompii. I spent at least 5 hrs in Pompii alone. (The trains are soooo slow). As you know ..pick pockets are abundant. Please read about this in one of Rick Steves blog. June can be very, very warm and no air conditioning in many of the trains. I know you want to see so much in so little time but take more time to smell the Roses and not fly through like a whirling dervish .

Hi,
Thanks all for the replies. I have decided to amend my itiniery for Italy. I will be doing 2 day at venice , skipping Florence for Rome for 6 days. If time permits I will do a day trip to Florence and pompei/amalfi. Hope it is a good trade-off.