Yes, that will work; we did almost the same thing last September with our son’s family. We left our apartment in Mürren by train and cablecar down to Lauterbrunnen, rode the little train to Wengen, and took the cablecar up to Mannlichen first. I love riding that cablecar UP; down not so much. At Mannlichen we spent over an hour at the playground for our 11-year-old grandkids, as we had done the hike to Kleine Scheidegg with them before. So we rode the gondola down to Grindelwald instead of doing the hike to Kleine Scheidegg.
You can do the hike and then either take the train down to Grindelwald Grund, or walk a bit further up to Eigergletscher and ride the Eigergletscher Express gondola down to Grindelwald Grund (which I would choose, personally).
From Grindelwald Grund you walk or take the bus through the village to the First lift. by now it might be lunchtime. You could find a place as you walk through town, or you could do as we did—-ride the First lift up to mid-station Bort and have lunch on the terrace at Berghaus Bort hotel and restaurant.
https://www.huettenzauber.ch/en/hotels-accommodation/alpinhotel-bort
Menus:
https://www.huettenzauber.ch/en/hotels-accommodation/berghaus-bort/restaurant?file=files/user_upload/HZ%20Betriebe%20%28Artikel%29/Alpinhotel%20Bort/Bort%20Speisekarten/2024/20240608_Basiskarte%20Alpinhotel%20Bort.pdf&cid=7368
The kids wanted to ride Trottibikes from here but there were none available til later, so we got back on the lift, rode to the top and hiked to Bachalpsee, then they rode down to the Trottibikes-bikes and my husband and I stayed on the lift and rode all the way down to town.
We traveled back to Mürren by train on the valley route, ending at Lauterbrunnen, and then cablecar and train back to our apartment in Mürren. It was a great day!