This is, oddly, one of the more manageable mountain regions in Europe for grandparents and small children — because the Swiss solved the vertical with machinery rather than expecting you to walk. Interlaken itself is flat: the Höhematte meadow, the Höheweg, the two river paths and both lakeshores involve no climbing at all. Jungfrau Railways does carry wheelchairs and pushchairs on the main Jungfraujoch route and much of the summit complex is served by lifts, but space per departure is limited and the arrangements change with the rolling stock — contact them before you travel rather than turning up and hoping. Your accommodation should hand you a guest card at check-in covering local trains and buses in the immediate area, usually with discounts on the Harder Kulm funicular and the Schynige Platte railway; confirm the details at the desk, because what the card includes varies.
Be honest with yourself about Jungfraujoch, though. Three and a half thousand metres is high enough that light-headedness and getting winded on stairs are normal rather than alarming — serious altitude illness is uncommon on a short visit, but it is not impossible, and anyone with a heart or lung condition should ask their doctor before booking. It is cold up there in July and the glare off the snow is fierce; proper jackets and sunglasses for everyone, including the kids, regardless of what the forecast says down in Interlaken.
The rest is honest caveats. Wengen and Mürren are car-free, so you move luggage from station to hotel yourself unless your hotel runs an electric cart — ask before you book. Trümmelbach Falls has a lift into the mountain but then wet, narrow, railed stairways inside the rock: not for wheelchairs, and not for anyone unsteady. The older cog railways have a step up from the platform that the newer gondolas do not. And the real constraint is weather, not mobility: a low-cloud day turns an expensive summit trip into a view of the inside of a cloud. Check the mountain webcams over breakfast and keep your summit day flexible rather than pre-booked to a fixed date. If it socks in, Bern is under an hour away on a direct SBB InterCity from Interlaken Ost and is flat, arcaded and largely indoors — the best wet-weather bail-out in the region.