My husband's driving, our children (Maddy, 6 and Jay, 10) are in the back, and I'm in the passenger seat, manning the stereo. Radio 4 and 5 Live have been vetoed, as Maddy claims that "all that talking makes me feel sick" – and while nobody's really convinced this is true, we're bucketing forwards in a metal box at good speed, and a backseat tantrum might be the last thing we hear before crashing and dying. So we've diplomatically decided to compromise and put a CD on. There's only one in the car that passes the Maddy test, and it's Nicki Minaj's Pink Friday.

Everyone knows Ms Minaj has a spectacularly dirty mouth. You might know that because she gave some of her Twitter followers the full chew-you-up-and-spit-you-out treatment when she was criticised for pulling out of V Festival with strained vocal cords earlier this month (sample hashtag aimed at the haters: "#gofuckyourselves"). You might also know it because Pink Friday comes with a parental advisory sticker on the artwork, unless you had the foresight to pick up the clean version. I didn't need to be told, because I'd had Did It On Em ("Man I just shitted on 'em/Put your number twos in the air if you did it on 'em") on my iPod for more than a year. I cannot get enough of Minaj's super-nimble, super-aggressive, super-profane raps. And that is why I'm sitting in the front of the car, finger on the skip button and twitching like Tipper Gore in the grip of a seizure.

There's a bit of swearing in the opener, but I let it fly. Then we're into the hard stuff with Roman's Revenge, which makes it up to "I'm a bad bitch, I'm a cu …" before my index on censorship calls time. That means we dodge Eminem's contribution: "Tied her arms and legs to the bed/Set up the camera and pissed on her twice/Two pees and a tripod!" – which shocked me into splutters of laughter the first time I heard it, and can also be elaborately excused as not literally about a woman, but about a female personification of life (aha, clever as ever, Mathers), and which all the same I don't fancy explaining to my six-year-old, thanks anyway.

Did It On Em is next, so we skip past that too, and by then I'm so inured to the cussing that the most objectionable thing remaining is will.i.am's appearance on the Buggles-sampling Check It Out. When we get to Girls Fall Like Dominoes – in which Minaj celebrates the devotion of her female fans – the promise that "If you're pretty / I sign titties" sounds like a straight up declaration of girl power, though I'm still lucid enough to make a mental note: when Maddy goes back to school, fleece her for Sharpies. My daughter takes her friendships seriously, and if she's picked up the message that chest scrawling is a mark of girl-on-girl loyalty, I can look forward to some pretty awkward convos in the schoolyard.

Minaj's ultra-stylised Harajuku Barbie look (high cleavage, poker-straight hair dyed pink, and immaculate pout) has a particular draw for small girls, as you can see from her 2011 appearance on Ellen, with two British girls whose homebrew cover of Superbass became a YouTube hit. The amazed infants cling onto their heroine like delighted limpets, and Minaj seems completely at ease with them. No effs, no jeffs, just open arms and big smiles.

I can tell my daughter is also besotted from the way that, at odd moments during the day, she'll hit me with a Minaj question: how old is Nicki? What colour is her hair really? Where does she buy her clothes? Maddy has joined the legion of Minaj-worshipping Barbz. I, of course, am intensely wistful for the days when she just wanted a cardigan like Sarah Jane's from Doctor Who.

But I'm overreacting. I grew up on my dad's collection of blues, soul and girl-group pop. Family legend says I toddled round the house singing Dust Bowl 12-bars, but I've never killed anyone's milk cow, dusted anyone's broom (until I was a decent age, anyway) or chucked my fish juice around at a wang-dang-doodle. Roman's Revenge plays it way over the line with violence against women, but I can remember rooting out He Hit Me (And It Felt Like A Kiss) by The Crystals from the Phil Spector box set, tra-la-la-ing along to its girlish embrace of domestic violence, and then never feeling sad when my boyfriends failed to give me a "loving" sock in the face.

For me in my cosy bedroom, it was Grand Guignol drama and camp, and that's what pop music sometimes is: a safe way to let the dark stuff in, before you're really ready to understand it. Still, it's something best done on your own, with headphones, rather than shared with your parents. Which is why my finger is firmly on the skip button for now, keeping Nicki (sort of) clean.