We've taken our children to the Berner Oberland when they were both that young (on two separate trips). They loved it. We didn't take them to any super high altitude places, like Jungfraujoch, just to be safe. We found a number of great hiking trails were we could push our jogging stroller and the toddler could safely/comfortably walk on his own (Murren to Grutschalp was one, Mannlichen to Kleine Scheidegg was another). The playground in Interlaken was easy to find and had great equipment for kids that young. Our toddler especially loved that he could watch the paragliders (he called them 'balloons') landing in the field next to the playground.
You will want to watch them carefully in places like Murren, as there are not a lot of barricades to keep them away from cliff edges, but we didn't find that to be too much of a problem. We took the Brienz-Rothorn Steam Train to the top of the mountain when our oldest was 2.5 and he loved every second of the trip. On a rainy day we went to Bern and visited the fountains (fountains are always a hit with our kids) and the Bears, which they loved. We went to the Ballenberg Open Air Museum on another rainy day and they had a great time seeing the animals.
If it gives you peace-of-mind (my husband would want to know things like this), we had to visit the hospital in Interlaken on one trip (not for the kids) and English was widely spoken and we were treated exceptionally well.
Enjoy your trip!