Indeed, as you proceed toward Kleine Scheidegg, the gravel is ripe for slippage. That is why I mentioned the issue of slippage in my early posts. In fact, that is why I posted those images, to make sure you knew what the trail was like. Then, as you provided more information, I moved toward the suggestion of starting out along the trail for a short distance and then turning back. I don't think that the trail would be a problem, but, of course, you know what is a problem or is not much better than I.
However, what you may have missed, is that near the Männlichen (LWM) upper lift station, and from there to the restaurant, and beyond at least as far as the playground and the lift station GGM (Grindelwald Grund Männlichen), the trail is paved. No gravel. Take a look once you get up there. At some point it switches to gravel, just beyond the lift station GGM mentioned by Traveljet (for the ride down to Grindelwald) which is just past the resataurant and near the playground, but the trail is still almost level for about a km.
I'd suggest that you rent some hiking staffs from one of the Intersport stores or other sporting goods stores...your hotel can suggest which one, or may even lend you hiking staffs. Take the staffs with you. Once you get up to Männlichen, take a look for yourself. Even if you only go to the lift station GGM for the ride down to Grindelwald, or only as far as the restaurant, or even don't leave the lift station LWM, you'll have great views. If the paved walkway or the trail looks OK to your parents, then you can go along it for a while, then turn back.
If you can get up there and see some of those views, you will have seen some of the best alpine views in Switzerland, and have a nice lunch or cup of coffee or tea while you are at it.
This link gives you an aerial view of the layout. Cows included
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