My children’s babysitter stayed over this week after I went out late one night. Since my children were born, we have seen her every day bar the weekends. Officially, we are now divorced; after the summer, my children were old enough to go to after-school club and our babysitter found a new job. In truth, I am finding it hard to let go. “I can’t let go!” I wailed to her this week. Wearily, she agreed to come back.

She has contrived not to notice when I’ve come in late, wasted ('everyone does it in England,' I say defensively)

The babysitter relationship is difficult, and difficult to talk about. Even if you do everything by the letter – pay your babysitter on the books; file the correct tax records so she can claim unemployment benefit, remain scrupulous about overtime and don’t do things like carry over unused hours from one week to the next – exploitation and resentment are baked in. There are no written contracts, and the labour pool, at least in New York, is deep enough for even the most secure babysitter to live with the threat of summary dismissal and replacement.

And there is, of course, the weird emotion of it all. This is particularly true if you are a single parent and see your babysitter with greater regularity than any other adult. We are not friends, not really. But every day when I come in we talk about Donald Trump, or corruption in her home country, or deficiencies in the New York education system, and of course we talk endlessly about my children. When she is stressed, I am sympathetic, while keeping one eye on the meter. When I’m stressed, she is sympathetic, while trying to get a foot out the door. The combination of intimacy and dependence, power imbalance and cost – at least $400 (£325) a week, even after the kids start school – guarantees a degree of dysfunction.

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Anyway, we are parting ways. There is no ceremony for this. Losing someone who has been in our lives every day for four years – who has contrived not to notice when I’ve come in late at night wasted (“everyone does it in England,” I say defensively), whom I have bailed out and who has bailed me out countless times, whom I have snapped at and felt hideously guilty about, who finds me infuriating and incomprehensible; someone to whom I am forever grateful and no amount of money is too much to be paid, whose life is infinitely harder than my own and yet the cost of whom has crippled me for years – is not an easy transition to make.

“I’m having separation anxiety,” I told her on Wednesday. “I can’t do without you!” I said. This felt simultaneously true and also like the proper thing to say, a formal recognition of how much she has meant to us. Now that we were through, we looked at each other with frank affection and a certain amount of relief. It was – regrettably, thankfully, bafflingly – finally over.

• Emma Brockes is a Guardian columnist