Strategizing a day trip to Zermatt; What's your general advice about bad weather/rainy conditions?

Based solely on the travel time (you know it's several hours one way, right?), I would not go from Murren to Zermatt for a day trip no matter what the weather is.
But, just fyi, there are convenient web cams to help with planning visits. There are so many great things you can do in and near Murren, you really don't need to overextend this way. Alternatively, you could go to Zermatt for a couple days--share your departure and entry points if you are open to shifting around the itinerary.
We had one day of rain, and we went to the Schilthorn anyway--it was snowing up here, and we thought it was really cool to experience it that way. We also went on a sunny day to enjoy the views. We enjoyed a sauna on our rainy day as well. Another thing we could have done is go down to Lauterbrunnen and walk along the waterfalls, as that would have been relatively easy to do with rain gear and it's a flat walk.
What month is your trip?

Absolutely (and I should have included this information), we are going to be in Switzerland from May 29th through June 7th. I had no idea it was as far away so, yes, any suggestions on how to gameplan it as well as possible would be appreciated.

Yep, too far for a day trip, but with nine days you could do both. I'd just keep reading at this point until the plan becomes more crystalized, but it's never too early to play around on the train website, SBB, as train travel (and cutting costs) is a huge part of Switzerland planning!
I chose between the two and went with Murren, but if you want to do both, I'd want at least three nights in Zermatt and to account for the travel time. That way, you have two days to choose from in case of a cloudy day. I don't think nine days would be too long in Murren though!

Thank you so much @valadelphia! Looks like we'll be splitting some time up between the two locations. ;D

Just to give another perspective. As someone who lives here I take day trips of this length and longer often. I like to see all areas of Switzerland and am not able to stay in hotels all of the time.

Travel time one way is 3h 15m, with many connections. Part of this is because of what it takes to get in and out of Mürren.

Positive side of doing this:

You watch the weather, when a good day is forecast for Zermatt, plan on going and check again the morning of travel

Make the journey without luggage, bring snacks, sit back and enjoy

Experience another part of the country on the best day possible (good weather)

I was in Switzerland last June and did a day trip to Zermatt from Montreux (2.5 hours each way) and it was one of my favorite days. Many people go to Switzerland just to ride the trains and enjoy the gorgeous scenery.

The trick with the Matterhorn is getting to Zermatt as early as you can. I believe I left Montreux around 6:30 am.

When checking the weather in Switzerland, do use the meteoswiss app or website as that will give you the most accurate prediction. For some reason, the weather channel app always shows rain in Switzerland.

I have my trip reports posted if you’d like to read them for some ideas. Just click on my name

But consider, Are you going by yourself, or taking three teens…at the crack of dawn? I guess they can sleep on the train, but I’d rather go paragliding (which I’d never do in a million years, lol)

I looked at my itinerary and I could add a couple/few days by staying in Zermatt or staying closer north towards Zurich. From the sounds of it, it looks like Zermatt could be just what we all need. (And we like zip lining and I see rappelling could be done too)

Be aware that usually the weather forecast cannot be relied on more than a couple of days out. And even then... So looking at a whole week and deciding based on that is not really going to work. You need to look at the sky...

For example: Here in Wengen todays forecast says something completely different about what the weather is going to be today than yesterday's did...

Unfortunately, you can’t always plan around the weather and hotels often need to be booked in advance. Hope for the best, plan for the worst. There are other things to do in Zermatt besides looking at the Matterhorn. So, I think you can still have a nice time there if the weather doesn’t cooperate.

Not specifically for Zermatt, but for the Lauterbrunnen Valley area, we found a number of good rainy day activities last fall because we had an inordinate amount of light rain and overcast days. We were seldom wet, but the percentage of days with limited views was higher than usual (we go annually).

• Get a Berner Oberland Regional Pass for each person. You can use it for “joy riding” on a day when the weather isn’t what you want and also for all of your other train, bus, lift, and boat travel. I have a route that took us most of a day to go from Lauterbrunnen over Kleine Scheidegg into Grindelwald for lunch and shopping, then back up to Männlichen and down to the valley. The scenery was terrific even on a somewhat rainy and very overcast day. Without a pass it would have cost CHF 135 per person. With a pass, nothing extra out of pocket.
• Tour the three towns: morning in Wengen, lunch in Lauterbrunnen with a walk out to to Staubbach Falls, then back to your digs in Mürren.
• Walk the valley from Stechelberg to Lauterbrunnen. Beautiful in any weather.
• Take a lunch cruise on the Brienzersee or Thunersee. Cruise included with pass, food sold separately.
• Hike along the river from Lauterbrunnen to Wilderswil and have lunch at Luca Piccante (fabulous Italian). You can also hike just the half from Zweilutschinen to Wilderswil then extend to see the castle ruins about 20 minutes from Wilderswil,

I meant to add to the rainy day list, checking out Thun. This is a bigger town with many nice shops and beautifully situated on the Brienzersee.

The Matterhorn can be shrouded by clouds even on a day that is clear all around—-it makes its own weather. So even a good weather report will not guarantee that the mountain will be “out”.

A few years ago we spent 3 nights/4 days in Zermatt at the end of June, and experienced the whole range of weather—-light rain, snow , and clear blue-sky days with or without clouds surrounding the mountain itself. Fortunately we had booked an apartment with a full-on view of the Matterhorn, and while in the apartment in the morning and evening we could watch the clouds come and go. During the days we went hiking regardless of the weather—day I hiking in a blizzard, day 2 in mixed clouds and sunshine, and day 3 with sunshine and clear views of the Matterhorn all day long.

As you have discovered, Zermatt offers a good array of adventure activities, so your family could happily spend several days there. That is the best way to have a good chance of seeing the Matterhorn.