At first glance, The Justice of Bunny King looks like it comfortably slots into a familiar category of earnest, sincere dramas: woman fights social services to get her kids out of foster care. That’s a bit of a movie cliche, and there are a couple of scenes here that you may feel like you’ve seen before. But first-time feature director Gaysorn Thavat brings real depth and layers of emotional intelligence to the issues, and her film is unexpectedly funny. It’s a match for the Australian actor Essie Davis, whose role as Bunny King is her best since The Babadook.

Bunny works as a “squeegee bandit”, washing windscreens on a busy stretch of road in Auckland, New Zealand. She is sofa-surfing, staying with her sister’s family while saving for a rental deposit , as she needs secure accommodation to get her children back. Looking at Bunny’s jar of shrapnel, you sense it’s going to be an uphill struggle. But she is someone who walks on the sunny side of life. That in itself is a bit trite: the relentless optimist. It’s a measure of Davis’s performance that Bunny seems absolutely authentic; a real-feeling woman not a character study.

The story of how her children – five-year-old Shannon (Amelie Baynes), who is disabled, and 14-year-old Reuben (Angus Stevens) – were taken into care, emerges painfully. It involves domestic violence, and what’s clear is that the justice system has been viciously unfair to Bunny. At contact sessions with the kids she is affectionate and excited, almost childlike herself. But she has a self-defeating streak of anger, lashing out at social workers.

The strength of the writing is in portraying Bunny’s reality, allowing us to wonder – like the social workers – whether she really is a reliable parent. This is thoughtful film-making, though I didn’t quite buy into the explosion of drama at the end.

• The Justice of Bunny King is in cinemas 11 February.