Travel

How many nights on the ground do you have?

Night trains are disappearing, due to cheap and efficient flights. But I don't think that will save you much time for your itinerary.

What source are you using for train schedules?

We are there 6 nights in Switzerland and 6 nights in Italy!

If you only have 6 nights in Italy, I would only do Florence and Venice...

You are losing some time making a fairly long journey from Interlaken to Florence.
There are many stops/changes in route and think it will eat up a good amount of time one day to do. There is a night train option for this route but looks like it may have multiple changes involved so you would not get any rest.
Cinque Terre would not be on the way, since you would be headed to Milan and then from Milan can catch a high speed train to Florence.

With 6 nights in Italy just do Florence and Venice, skip the Cinque Terre this time, that is not that much time even for them.
I would say your Swiss destinations do not need as much time as the Italian ones. With travel time taken out, you really only have 2 days in Florence and 2 days in Venice ; not sure why you think you have time for a 3rd Italian base?

Or skip Lucerne, condense your time in Switzerland to 1 night Zurich, 3 nights Interlaken. Then go to Florence for 3 nights, Cinque Terre for 2 and then Venice for 3 nights at the end. You could also look at Cinque Terre before Florence but think that would mean a really long travel day to get from Interlaken to Cinque Terre in one day.

There is no overnight train between Switzerland and Italy (and has not been for years). It does take 7.5 hours or more to travel from either Lauterbrunnen or Luzern to Monterosso. On the plus, side, the train connections go quite smoothly.

With six days in Switzerland, I would spend the first two days in Luzern, it is about an hour from Zurich and is a better city than Zurich. Four days in the Lauterbrunnen Valley (Murren or Wengen), it is located up into the mountains from Interlaken.

Luzern, 2 days,
Lauterbrunnen Valley, 4 days,
Train to Florence, 3 days,
Venice, 3 days.

I hope you leave late morning from Venice, getting to the airport early can be difficult so you need to plan ahead.