A Quick trip to Switzerland in March

You do realize that you will be going during ski season, and Lauterbrunnen and Zermatt hotels will be getting top dollar. With 7 nights and 3 allocated to Luzern, I'd pick either Lauterbrunnen or Zermatt, and I would lean toward Lauterbrunnen. More things to do (assuming none of you ski or snowboard).

arrange for a transfer to Lucerne for 3 nights

You do realize it is a 1 hour direct train from Zurich airport to Luzern.

Do any of the three of you ski?

What is it that draws the three of you to Luzern, Interlaken or Lauterbrunnen. Or Zermatt? You say " I have been to Switzerland but others have not hence Zermatt" but I don't get the "hence". I've never known it to be a requirement. I'd much prefer to be up close with the mountains all around than one overpriced and remote one.

Everybody is different - that's why I ask the questions - but I have been to Switzerland many many times, and most years included the Berner Oberland of the Lauterbrunnen Valley. I've visited Zermatt once and have no plans to return.

YMMV

If you haven't already done so, you'll probably want to research the average weather in March, esp. at the elevations/locations you're planning to visit. The locations you mention vary significantly in elevation above sea level. A rule of thumb (that works better if not in large mountain ranges) is that temperature decreases 3 to 4 degrees (F) for every 1,000 feet you go up. But being in an area of large mountains, makes it more difficult to predict weather since large mountain ranges often generate their own weather.

Instead of Switzerland for your mountain vistas, have you considered Austria a little to the west?
You can get to Innsbruck easily on the train from Munich. And the mountain scenery there is absolutely breathtaking.
When you're ready to go onto Venice, you go through the Brenner Pass on the train and it's a straight shot into Northern Italy.
We find the Western Tirol much easier to travel through and it's much less expensive than Switzerland.

I think the option to head toward Austria after central Switzerland is a good one. From there you can go to Venice, or first go to Verona then Venice. I would skip Milan unless there is a reason you need to go there.

We vsited Switzerland late February though early March 2017. A serendipitous event in Luzern was the Carnival Monday celebration. the 2019 Carnival Monday takes place March 4, 2019.

During our late February/March visit the low elevation cities such as Luzern were snow free and cool but comfortable temperatures. The high elevation ski towns were snow covered but villages do a great job of snow removal from pavements and streets. We brought our boot chains but didn't need them.

We enjoyed the Bernina Express train excursion departing after breakfast to Italy for a lunch stop and returning in time from dinner:
https://www.myswissalps.com/berninaexpress
The Express journey was a great rest day activity.

My wife and I got round trip tickets to Zurich for about $400 each, so we booked them (last week of April). (We have friends that live there, so we are going to visit them)
AFTER I purchased the tickets, we began planning - I reviewed the temperatures for major sites that we're interested in and for the middle section of the time, we're going to Naples, Italy - I wanted some warm weather.
I've been to Grindelwald and want to bring my wife there sometime, but I think we need to wait to mid May for good walking-around weather.

Thanks for the great feed back. Our concern now is point to point or a pass or a Swiss Pass. I am looking forward to going back to Switzerland, it's been awhile, and seeing through my daughter and granddaughter's eyes will be fun. Travel is a great way to have some shared experiences.