Mike Melody shouldn't be alive. In 2012, diagnosed with motor neurone disease, he was given a maximum of five years. His artist daughter Victoria began planning his funeral, even penning a eulogy, to sum up his life, but he's very much still with us. Doctors got him wrong.

After two hours of him in this off-piste comic treat, it's clear that's Mike Melody to a T: a difficult bugger who defies all diagnoses. A former television antiques expert, once fired for yawning in David Dickinson's face, he's headstrong, impulsive and honest to a fault – all of which tends to derail his daughter's new show.

Victoria Melody had set out to stage a living funeral for her dad, a celebration of his life while he's still here to see it, as a way of examining our attitude to death. She'd even gone so far as to train as a funeral director in Port Talbot, sewing lips shut and watching bodies burn down, to fully come to terms with the subject – the practicalities, emotions and finances of mortality. Imagine Stacey Dooley's oddball older sister and that's Melody: curious, clutzy and all kinds of winsome.

You can see the threads of her thinking - something that ties together humans and objects, old-age and antiques, to question the way we evaluate life. She puts her dad through the Co-op's standard funeral questionnaire, hires a house band to play the blues songs he loves and delivers her eulogy with good humour and warmth. There was the time he crashed his car into a cow and the drinking session during which he – accidentally – bought a house.

Only Mike Melody's not the neatly surmisable sort – and light-hearted anecdotes about his eccentricities are only half of his story. To give a sense of him, he's around 70, with lank grey 1970s hair, a chain-smoker's pallor and a limp left arm thanks to partial paralysis. He laughs like a drain, distracts easily and cannot help but take the piss. He's a thrilling theatrical presence onstage – unpredictable as a bomb that might blow any second – but, my god, he must have been a difficult dad.

Disputing every detail of his daughter's account – an aspect that asks whether we control our legacies or know ourselves – he demands a different funeral (and a different show), wresting control of the second half himself.

It makes for a mongrel piece, as messy as life, as awkward as death and as funny as anything spinning out of control. Like the best of plans – like Mike Melody himself – it derails itself again and again, rarely finishing a point or tying up a thought. But if Ugly Chief gets nowhere near the neat narrative arc it aspired to, it's far better for it: bumpy, testing and full of contradictions. In that, it's a fuller testimony to Mike Melody than any eulogy: an upfront reflection of his flaws, his foibles and his cack-handed fathering skills that, nonetheless, captures his human heart.

Antiques aren't just objects, they're things with stories. They fall in and out of favour and go up and down in value over time. To know what they're worth, Melody explains, you have to know their full history. People, it turns out, have provenance too.

Ugly Chief runs at the Battersea Arts Centre until 18 November.