The novel satirizes Victorian marriage conventions, often in very dark ways. For example, a scene in Chapter 4 makes it clear that while David's mother and Mr. Murdstone's marriage conforms to many Victorian conventions, it is also a marriage gone very wrong:
‘It’s very hard,’ said my mother, ‘that in my own house—’
‘My own house?’ repeated Mr Murdstone. ‘Clara!’
‘Our own house, I mean,’ faltered my mother, evidently frightened – ‘I hope you must know what I mean, Edward – it’s very hard that in your own house I may not have a word to say about domestic matters.
In an ideal Victorian household, a husband and wife each had their own roles. A wife was never the legal owner of the house, but was rather protected by her husband. Even when a woman brought family property to a marriage, her husband immediately became the owner of that property. Although it might revert to her family if she died, this was only the case if the couple had no children. If there were children, the husband would keep the property until the children came of age.
Mr. Murdstone is technically correct that it is "our house" and really, as Clara eventually calls it, "your own house." Especially after Clara and Mr. Murdstone have a baby, he has a strong legal claim to it. Already, though, marrying Clara and assuming a parental role over David has given Mr. Murdstone the legal right to essentially steal the house from Clara. It's not just that Clara has very little recourse under the law to assert that the house is her domain—it's also that doing so would shatter the idea of her as an ideal wife. She is not supposed to be able to manage on her own but is rather supposed to keep the home in order according to her husband's wishes. She is skirting a line when she says that she is supposed to have "a word to say about domestic matters."
But for all his legal correctness, Mr. Murdstone abuses David and his mother. Eventually he seems to cause Clara's death. Clearly, an ideal Victorian marriage can go very wrong. This abusive marriage is a very dark element of satire. It is difficult to imagine laughing at it, but it might provoke some uncomfortable laughter at the delusion that this "ideal" system works in practice. By contrast, one of the most functional "marriages" in the novel is not really a marriage at all. The relationship between Miss Betsey and Mr. Dick is based on mutual respect and collaboration. The very fact that they are not married allows Miss Betsey to retain financial power, and it allows Mr. Dick to explore the benefits of working not to maintain a household, but because working is (at least in Dickens's estimation) a noble pursuit. Through the contrast between these two "marriages" (one "ideal" but abusive, and one not even real but far more fulfilling), Dickens invites readers to see the absurdities and pitfalls of Victorian laws and customs surrounding marriage.
In Chapter 22, Miss Mowcher the hairdresser shows off the Prince's fingernail clippings, which she uses to attract customers. This moment satirizes a society that is obsessed with appearances and social connections:
I always carry ’em about. They’re the best introduction. If Miss Mowcher cuts the Prince’s nails, she must be all right. I give ’em away to the young ladies. They put ’em in albums, I believe. Ha! ha! ha! Upon my life, “the whole social system” (as the men call it when they make speeches in Parliament) is a system of Prince’s nails!
It is ridiculous that Miss Mowcher can more easily get clients by showing off a Prince's fingernail clippings than by simply demonstrating her skills. Specifically, it illuminates her wealthy clients' obsession with image social connections. She claims that young women "put 'em in albums." It was common practice in this period for young women to keep albums, sort of like scrapbooks. These albums were meant to be shared, and they contained keepsakes from social events like parties. They could signal that a young lady's attention was in high demand. It was common to hold onto locks of hair from lovers or family members, but nail clippings were a bridge farther. Someone who held onto a prince's nail clippings in an album, especially if she had not even met the prince but only his hairdresser, was clearly trying to show off and stretch the truth of her social connections, like someone today clumsily dropping the name of a distant celebrity connection.
Unlike the young ladies of a higher social status than her, Miss Mowcher understands how ridiculous this behavior is and calls attention to it. She then describes the behavior as symptomatic of a larger cultural problem among powerful people. She criticizes the self-important language of men in Parliament, who do not see that they are governing "a system of Prince's nails." That is, nothing they are debating is as important as they make it out to be. The comparison implicitly goes the other way, too. Through Miss Mowcher's comment, Dickens satirizes society's obsession with appearances and social connections as at once laughable and also a grave issue Parliament should be working to resolve. If Parliament were less obsessed with appearances, they might put in place more social safety nets to ensure that lives would be less easily ruined by one wrong step. Steerforth laughs at the joke without realizing that he is at the butt of it, emphasizing that "important" people do not necessarily realize what the important issues facing society are.