If I ride along slowly, I can hear an angry rhinoceros snorting a few metres behind my bike. This is a reassuring noise because it means my son is managing to follow – registering his fury with hostile grunts, but still just about keeping up.
More worrying is silence, which suggests that he has abandoned all efforts to pedal, has climbed off the bike and is sitting cross-legged on the gravelly path. I stop, cycle back a little bit, look at my watch – it's 2.15pm – and wait for him to get going again. I breathe in the pine forest smells, feel the cool air from the mossy banks on my legs, smile, and then suggest in a friendly voice that perhaps he might like to stand up, put himself back on the bike and start riding it.
"Why should I?" he replies, seething. "What is the point of this?"
We are near the bottom of an Alpine foothill, the car is somewhere near the top, and the only way home is to cycle upwards. It is hard work for six-year-old legs, and I'm broadly sympathetic. I let him rest a little. By 2.40pm he is still sitting, angrily poking twigs and leaves under his sandal straps.
"Come on," I say, in honeyed tones. "Try pedalling a little."
He shakes his head, and bares his teeth. I leave my bike, put him back on the saddle, and push him and his bike up a bit further up the hill, stop, return for my bike, cycle up, and repeat the procedure. It is good exercise for me, and in this way we manage to get to a point where we can be rescued by a car.
Before I had Rose and William I liked to go on holidays that involved bicycling from one town to the next, or walking and staying in mountain refuges. Once they turned seven and six, I felt it might be time to try a holiday that involved more than lying on the floor fiddling with Lego pieces.
And I'm happy I did, because this part of the Swiss Alps near Flims is beautiful in August, and we walked, swam in lakes, and rode bicycles (slowly) through the forests. I enjoy myself tremendously, with the small caveat that my ears begin to wilt with the high-level complaining from the children. They enjoy themselves for reasons that have nothing to do with walking or cycling and everything to do with the swimming pool at Rocksresort, the apartment complex where we are staying.
Slowly through the week, their Olympian stamina for complaining is worn down, and they become unwillingly pliable, more ready to understand that resistance is pointless, and more mournful in their still-frequent attempts to understand why I am making them embark on daily epic journeys.
Flims is a ski resort that is also now a major major mountainbiking centre, with over 330km of signposted trails for all levels, from beginners to a new 7km freeride course. It also has a lot that is suitable for children of the age of my two. There is a tree climbing, rope-swinging centre (sportzentrum-flims.ch, family ticket CHF88 [£62]) in the forest, where they are hooked to safety ropes and set free to climb along planks through the tree branches. They love that. At the Freestyle Academy (freestyleacademy.com, adults £18, 13-17s £15, six-12s £10) children can have trampolining, snowboarding and skateboarding lessons, and hurl themselves off high walls into pools of foam blocks.
A few minutes' drive from town is Lake Cauma, with warm turquoise-green water. It is the end of August, most Swiss children are back at school, and the place is almost empty. We swim to an island in the centre of the lake, climb a rock and watch teenagers doing backflips into the water.
It has probably been a mistake to cycle here for lunch, because the route involved three or four kilometres of gentle descent. It will be a harsh uphill ride home. Throughout lunch, I feel anxious about the imminent onslaught: "Do you think you'll do a lot of moaning on the way back?"
There is a pause while they consult. "We think we probably will."
We hire bikes on two days, and make sure that on the second day we take a route that looks flatter – on the map. The map advertises route 249, as a "family-friendly bike ride" of 11.7km, taking an hour-and-a-half (flims.com/en/biken/tours/tours). As the week progresses, I learn to be sceptical about these timings. That route takes us four hours, and all our reserves of parental stamina are poured into cajoling the children to keep going.
I am impressed at my son's in-built spirit level, watching his spirits rise and fall with the incline of the hill. Happy singing is replaced instantly (as the path begins to slope upwards) with an unceasing, and fairly menacing muttered chorus that goes: "Why are you making me do this? You think I like this? Why do I have to do this? Is that what you call fun?" Then the road begins to tip downwards again, and the cheerful humming returns.
We take ski lifts into the Alps to follow walking routes that are also advertised as family-friendly. The waitress at the Cassongrat restaurant, at 2,675m, tells us the loop walk along a ridge of the Alps (flims.com/en/wandern/hiking-tours) would take less than an hour.
Ten minutes into the walk, my son announces: "I've had enough of this already. Are we nearly there?" Four hours later, I realise that the family- friendly designation applies only if you are a family of mountain goats.
Rocksresort is a very modern complex of square blocks of apartments made from grey stone. The architecture features in hotel design books, and the flats are very simply, and cleverly laid out, in bare concrete and wood. I feel a little sorry for the owners of the Laaxerhof hotel next door, an old-fashioned Swiss hotel with beautiful balconies exploding with red geraniums, whose views of the Alps are now obscured by the stark structures of the Rocksresort. But it is a very child-friendly and convenient place to stay, just by the ski lifts, and has several restaurants, one of which is serving a soup of freshly picked chanterelles.
On the last day, clouds drop low over the resort, and it begins to rain. When the weather clears, snow has covered the range of mountains visible from our window. We ride a ski lift to the summit and take great delight in being able to throw snowballs in August.
For a family with slightly older (or more athletic) children, a visit to Flims would make an ideal activity holiday. For children only a few months off stabilisers, it is fairly challenging. Next time, I'm going to investigate Holland.
• A two-bedroom apartment for up to five people at Rocksresort (rocksresort.com) costs from £78 per night this summer. EasyJet (easyjet.com) flies to Zurich, a two-hour drive or bus ride from Flims, from 12 UK airports from £55 return. Car hire in July from Zurich with Sixt (0844 248 6620, sixt.co.uk) costs from £26 a day
