"This is heaven," comes a call from a few feet away. I turn from where I am sitting on a jetty reading a Camilla Läckberg thriller, to see my nine-year-old daughter Eve, standing waist deep in the Swedish lake she has all to herself, running her hands dreamily through lilypads, sun in her hair. As Eve's current pre-teen rejoinder about most things is "This is rubbish", followed by a spectacular eye-roll, this is a special moment for me.

It has to be said that our family has not arrived in Sweden in the best of moods. A recent house move complete with last-minute lost cat, followed by the realisation, three days before our carefully booked budget flights to Gothenburg, that seven-year-old Ruby's passport has expired, has led to a week-long, group, family panic attack. We arrive a day late, hundreds of pounds poorer on not-so-cheap, re-booked flights, badly packed, with a mobile that doesn't work, and, for me, an overdue writing deadline to finish in a Gothenburg hotel with no Wi-Fi.

So when, on Day Two, I wake feeling inexplicably relaxed, it is perhaps not unreasonable to accuse my husband of slipping tranquillisers in my tea. Then I realise it's just Gothenburg.

I've never been to Sweden before, and only booked it because of my devotion to Scandi-crime. It was while watching Wallander that I developed a fantasy of staying in a cabin like his: cosy, quiet, with views over a meditative expanse of water under a moody sky, where, like the melancholic Swedish detective, I could wander out, and contemplate my latest murder (I am a thriller writer myself, I should explain).

What I'm not expecting, is to find that kind of peace and quiet in a Swedish city. Perhaps everyone else has cleared off to their summer cabins already, but the wide, handsome streets feel half-empty. Ruby and Eve share the dedicated play area of the Gothenburg City Museum with one well-behaved toddler, while we collapse gratefully on a big squashy sofa. At the Nordens Största Science Centre, each room is three-quarters empty, allowing the girls, for the first time in their lives, to see monkeys and sharks close-up without elbowing someone in the face. In the evening, in the old harbour, we sit outside chilled-out bars wrapped in provided blankets, the four of us chatting late into the light summer evenings. Everywhere we want to stop, there's a thoughtful seat: a bench, a free cafe seat, a comfy windowsill. It's all just so unexpectedly, well … relaxing. Without warning, the four of us start being much nicer to each other.

Detoxed from our stressful month in a remarkable three days, we pick up our rental car and head to our cabin. Although myriad summer cabins dot Sweden's 100,000 inland lakes and 7,000km of coastline, I discovered back in May that I needed investigative skills on par with Wallander to book one from the UK. We struggled to find more than one cabin rental website in English (sweden-holidays.com). And although there were some around the £400-500 a week mark, most were already booked. Panicking, we have therefore shelled out for a more expensive house, called Vängsö Sjögård, convincing ourselves that it's worth it to celebrate our 20th anniversary, and because my mum, who'll be joining us later, is celebrating a "special" birthday (if I say more, I myself will be murdered). You'd struggle to call it a cabin. More a house. Or an estate.

Which explains the reason we are now driving the 300 miles across Sweden in the cheapest rental car possible, and one apparently built for four mice, the girls' faces squeezed against the suitcase that sits between them, me with my feet on the dashboard to avoid deep-vein thrombosis. Sweden is certainly more affordable than it used to be – now on a par with France – but with steak and frites already spotted on a restaurant menu for £30, corners have had to be cut to make this three-week family holiday affordable.

Our house is an hour west of Stockholm, on Lake Nyckelsjön among gentle yellow fields and red barns, a few houses in the distance. The owners hand over the keys telling us not to worry too much about locking the doors. Although it is grander than a normal cabin, its setting is typical. Down at the lake, we find a jetty with two boats. We wade out into the murky but clean water, the girls shrieking at the odd sensation of cool, fresh water and silky mud on our feet. The water comes up to Ruby's chest. By the middle of the lake, it's still at her chest. Relieved, my husband and I realise we can lie on the jetty all day, and read books as the girls play safely in the shallow water. "Can we stay here all day?" they cry, leaping off the jetty with exuberant splashes.

Two days later, the sun is still shining and we've seen no one else on the lake. It's like our own giant, swimming pool. I take to swimming for half an hour a day across it.

Maybe it's the fresh air, but I start, very uncharacteristically, to run each morning along the quiet country roads. Combined with our visits to the supermarket to stock up on the salmon, beetroot salad, delicious rye breads and lingonberry juice that we supplement with the vegetables our hosts tell us to pick from their garden, I begin to wonder if this is the first holiday ever where I will lose, rather than gain, five pounds. It doesn't hurt, too, that wine is only sold in government Sytembolaget shops to encourage Swedes to be thoughtful about how much they drink. We keep forgetting to get there by closing time, which is 5pm. I'm starting to feel like I've had two weeks in a spa.

My mum and step-dad arrive for two nights, and we celebrate both birthday and anniversary with a barbecue and a midnight row across the lake, under a deep-pink sky. I watch Eve and Ruby's faces sparkling with excitement as we take long strokes across the silent water under swirls of purple and scarlet cloud, a family of geese spread in black across the sky. To their delight, we then strip off, and dive into the night-time lake. It is wonderful. Magical. I'm not surprised the Swedes want to keep this to themselves.

There's time at the end of our trip to spend a few days in Stockholm. With its swathes of tourists, it seems a little frenetic in comparison, but a sunny boat tour around the islands of the Stockholm archipelago to the royal summer palace of Drottiningholms makes us love it here even more, as we watch the relaxed Swedes canoe, and swim, and water-ski past us, skyscrapers in the background.

We drive back to Gothenburg for our flight home the next day, and stay up late in our hotel, enjoying a last night of Swedish tranquillity, overlooking the quiet streets below. Unexpectedly, I find myself a bit tearful at the thought of going home. Next year, we're booking early.

• Vängsö Sjögård, near town of Gnesta, Södermanland, can be booked through sweden-holidays.com, costs from €1,990-2,600 per week and sleeps 10. Ryanair flies to Stockholm-Skavsta airport, a 45-minute drive from the lake house, from Edinburgh, Gatwick, Liverpool and Stansted. Easyjet flies to Gothenburg from Gatwick and Manchester; Ryanair flies from Glasgow Prestwick and Stansted. Price comparison website carrentals.co.uk offers a week's rental from Gothenburg airport from £250

The Playdate by Louise Millar will be published by Pan in May 2012