Although the Malfoys managed to keep their lands and fortune, escaping going to prison for their loyalty to the Dark Lord ... sorry, He-Who-Must-Not-Be-Named ... because of Narcissa's lies and Draco's unwitting help, life has not been easy for them. Many of their former allies despise them, seeing them as betrayers, and as the reason the Dark Lord's brilliant plan ended in his death. On the other side, even those who fought for their acquittal don't trust them. The Malfoys, it is true, have always been on their own side first and foremost, and it is difficult to trust those whose loyalty is but to themselves.
All this would be fine – or at least, possible to deal with – if it weren't for the wars going on at home. Draco can handle the disdain of others; he's arrogant enough to ignore it, and to use his pardon to bully others on to his side if necessary. The constant fighting and increasing hostility between his parents, however, is both beyond his control and something he cannot simply dismiss. Despite having been quite reluctantly on the Dark Lord's side in the later months of the war, Lucius has convinced himself that he was a devout and passionate follower; Narcissa's betrayal of the Dark Lord when she lied to him about Potter is therefore a betrayal of Lucius and their family. Draco, Lucius treats with contempt: Potter's victory is at least in part due to the fact that Draco was too weak to keep Potter from disarming him. Lucius has no time for such a disgrace to the Malfoy name.
Draco's honestly not sure how he ended up here at Margate. It had been a particularly difficult day, involving screaming fights between his parents, threatening his father when he'd attempted to hex his mother, having Goyle turn his back on him when he abandoned the house, and listening to Pansy tell her mother coolly, "It's no one," as she shut the door in his face. He remembered standing there, knowing that there was no one he could turn to and nowhere else he could go. He remembered his fist clenching around his wand as he closed his eyes and wished, for one desperate moment, that he could just find somewhere he was free, and safe, and away from all this!
And he stumbled, despite not moving, and opened his eyes, and found himself ... here.
Draco's not sure how it happened, but he must have stepped away from Pansy's door somehow, because now he's stumbling through sand, and there's the sound of the ocean in his ears. He's never heard of Apparating without knowing exactly where you wanted to Apparate to, but he's pretty sure that he hadn't planned on finding a beach, somewhere in southern England, from the feel of it.
It isn't until he tries to Apparate back home ... or rather, to a piece of Malfoy property that had been his hideaway of choice, lately ... and can't, that he begins to wonder.
Honestly, though, he's too tired to wonder for long. Instead, he finds a rock, and sits, and feels hollow and fragile. He'll deal, he'll remember he's a Malfoy ... but later. Right now, it's just all too much.