Do I have time for this in one day?

You are arriving from where? Montreux? If so, you could save a bit of backtracking by exiting the train at Spiez and storing your luggage there and then proceeding to Kandersteg to get to Oechinensee from there. You can do Harder Kulm later if you have time, or on another day.

Yeah I am coming from Montreux - I thought the Golden Pass Express didn't make stops along the way though - apparently I need to look back into that haha because that makes more sense to stop in Spiez and not have to backtrack to it...

Yes, it stops at Spiez at 10:21, and the train to Kandersteg is at 11:12, so that will give plenty of time to store luggage in lockers there.
Have a supply of 5 franc coins for the luggage lockers.

How many of you are there? If you all want to sit together, seat reservations may be recommended on the GPX.

Just a heads up…. We arrived at Interlaken Ost at noon this Monday and all the lockers were in use-good luck

Thanks so much for the helpful info. And ah good to know about the lockers - what did you guys end up doing with your stuff did you just lug it around with you? That's such a bummer!

And @Sam that's a perfect plan thanks. I mistook the goldenpass express train "not changing trains" for not having stops haha. Now looking closer at the route on SBB I see the stops and that looks perfect to get off in Spiez, thanks for the heads up and making that much more efficient for us!

Yes, way too much. And I wouldn’t do Harder Kulm at all, even if it wasn’t too much. There are better places to see views that aren’t just a tiny crowded platform and a crappy restaurant.

@wanderweg good to know! I don't love stuff like that haha so I appreciate the advice - we'll skip it! Is Schilthorn the same, not worth it and should be skipped - or is that one worth going up to later while we're in Murren do you think?

@wanderweg since you're really familiar with Murren do you mind telling me your opinion on these different walks/hikes (or anything I'm forgetting) in the area. Just starting to plan out what to do or skip while we're in Murren (and what is best to walk for the experience vs when to take gondola to make it easier). Since I'm at the beginning of planning these out I'm not familiar with the areas yet so forgive me if any of these ideas are bad haha :) And feel free to give any advice you think of!

Note: We don't want anything too hard because we have kids (and if it's just as good to take transport there then we should do that), but still want some beautiful hikes and don't want to miss out on any hiking that's especially special! :) And our kids are good sports with hiking!

Options:
Walk from Murren to Winteregg (30 min)
Walk from Murren to Grimmelwald (35 min) or go to Allmendhubel first then walk to Grimmelwald (not sure what route is better or if it matters)
Hike from Allmendhubel on Northface trail (I think this ends in Murren? Or if there’s a different route you recommend, easier is probably better. But also good with pushing the kids to do hard things so we can see beautiful things together!) or any other hikes from Allmendhubel.
Hike from Wengen to Lauterbrunnen (1 hr)
Hike from Wengen to Mannlichen (need to look this one up) and then to Kleine Scheidegg

Schithorn/Birg is not a waste of time, not in the same category as Harder Kulm :) It's busy, but it's still worth it.

Walk from Murren to Winteregg (30 min) -- walking the wrong way, easy and stroller friendly, but if you're going to do it, train to Winteregg and then walk to Murren as views are better this direction. This isn't a priority walk, it's just a good filler for average weather days/relax time. Not a thing to prioritize above bigger things.

Walk from Murren to Gimmelwald (35 min) or go to Allmendhubel first then walk to Gimmelwald (not sure what route is better or if it matters) -- You have your routes mixed up on this. Murren to Gimmelwald is a nice walk, stroller friendly and realistically takes more like an hour, not 35 min unless you never stop for photos or enjoyment. Good option. Allmendhubel doesn't factor into this.

Allmendhubel/Northface trail -- Allmendhubel + counterclockwise Northface is my favorite hike for beginner/intermediate. Allow time to play at Allmendhubel. There is really only 1 fairly short uphill portion, so you should be fine. It's the best bang for your buck. It's more of a true hike, whereas the ones above are walks. If you only do 1 hike in Switzerland, I'd say this is a great option. This is the route but DO NOT do the Sprutz detour, not worth it - https://swissfamilyfun.com/murren-northface-trail-sprutz-waterfall/

Hike from Wengen to Lauterbrunnen (1 hr) - A definite no. Steep downhill and below average views. Way better options above.

Hike from Wengen to Mannlichen (need to look this one up) and then to Kleine Scheidegg - You absolutely cannot hike from Wengen to Mannlichen with kids, don't even consider it, take the cable car, enjoy the playground and then walk to Kleine Scheidegg before taking the train back to Wengen and then continue on to Murren. This is a great option, easier than the Northface, more of a walk, but with great views and a great playground. A really good option.