Painting Family: The de Brays, Dulwich Picture Gallery, London

Jan de Bray's Banquet of Mark Antony and Cleopatra is an odd work, but then it was meant to be. The canvas is a portrait historié, a portrait whose subjects are shown as historical characters – in this case, a licentious Roman general and an Egyptian queen whose husbands included two of her brothers. Hardly a flattering depiction, especially given the identity of the sitters: Salomon and Anna de Bray, Jan's father and mother.

Around the elder de Brays are arrayed the artist himself – the half-hidden man to Cleopatra's right is probably a self-portrait – together with various other of their 10 children, roped in as extras. The Banquet of Mark Antony and Cleopatra was painted in 1652. In 1663-64, an outbreak of plague in Haarlem killed Salomon de Bray and all but three of his living offspring, one of them Jan. By then, Jan had buried two young wives and would bury another, along with his only child, a son. Like the story he had painted a dozen years before, all would end in tragedy.

What we see in the Banquet of Mark Antony and Cleopatra is an elision of life and art, and not just in the work's coincidental endings. Jan was 25 when he painted the picture, and he had learned its Dutch classicism from his father. Two of his brothers, Dirck and Joseph, were also Salomon's students and would work in his studio. Art history tends to be impersonal, its currents and countercurrents put down to sociology, economics or Hegelian dialectic. It's easy to forget that art was also formed by the dynamics of the family – an oversight that the Dulwich Picture Gallery's excellent show, Painting Family: The de Brays, aims to correct.

The Carraccis, the Bellinis, four generations of the Teniers; all those artists designated The Older or The Younger, père or fils; these, too, shaped how art was made. The family is Freud's battleground, and it is tempting to see the Banquet of Mark Antony and Cleopatra with a Freudian eye. Netherlandish art may have been full of winks and nudges, but depicting your parents as a traitor and a whore was going it even so.

Salomon was 55 when his son painted him as Mark Antony, an old man for his day. His early career had coincided with those of greater Dutch painters such as Gerard van Honthorst, one of a group known as the Utrecht Caravaggists. Salomon's Martyrdom of St Lawrence, done in the same year as his son's portrait historié, looks as though it was painted 20 years earlier. Four decades after Caravaggio's death, its concerns are still the Caravaggist ones of conjuring light out of darkness.

There's a bit of vestigial Caravaggism in Jan's Banquet of Mark Antony and Cleopatra, but the younger man's light is more fluid, less sculptural, newer. One of its effects is to push Jan's self-portrait into the shadows, although the directness of his gaze – he's the only adult to meet our eye – means that he's anything but overshadowed. The Banquet of Mark Antony and Cleopatra exists in two worlds, one of classical antiquity and classicist painting occupied by Salomon, the other of the present and the new dominated by Jan. It is a portrait not just of a family but of yesterday's man and tomorrow's, the latter biding his time. Jan might as well have painted his father as Laius. His intent could not be more Oedipal.

Where was all of this leading? It depended on which de Bray you happened to be. Salomon's elder son, Dirck, avoided competing with his father by painting flowers and still lifes. His Still Life with a Dead Rabbit and Falcon in a Niche is a minor masterpiece, but it is minor. Joseph, the youngest, had the shortest career, dying from the plague at 35. Like Dirck, he seems to have been an adept painter of still lifes, although his work in this show is charming rather than great.

It was Jan who got out from under, surpassing his father to become one of the finest Dutch history painters of his day. In the rooms given over to his work, we see him playing around with Rubens and Helst and fellow Haarlemite Frans Hals – with anyone except Salomon, in fact. Jan's later allegories and mythological pictures edge towards greatness. You wonder what would have happened had his son lived; what a third generation of the painting family might have done.

Dulwich Picture Gallery, London SE21 (020-8693 5254) to 5 Oct