The four principal characters are Sophy, Sam, Mr. Twycott and Randolph. While all characters act as a unified whole to reinforce Hardy's central themes, one of which is the tyranny of ironic random, chance events (though some may prefer to understand this theme as the inevitability of predestination), the characterizations might be read allegorically with a discernible theme assigned to each.
To find reflected themes, examine their characterizations to expose a reflected theme. One set of possible themes follows. You can make similar analyses of events, personal traits, names, and behavior to find other themes reflected by these characters.
First, let's establish that Sophy is not romantic. She accepted Sam's marriage offer but when asked by Twycott if she wanted to marry, she replies, "Not much. But it would be a home for me." Now, Sophy may most reflect the theme of the tyranny of ironic chance and random events (again, some may prefer to think it predestination though there is little to no textual support for a religious reference).
Sophy's life is governed by four chance events: (1) Twycott's decision to reduce his staff at the same time Sam proposes marriage; (2) a quarrel with Sam; (3) Twycott's illness; (4) Sophy's fall down Twycott's stairs. Everything in her life occurred because of these events that she had no reasonable control over. It matters here that Sophy is not a romantic because it is clear she made reasonable, practical decisions at each turn of events.
We don't know the backstory of why Sam and Sophy argued, but, because of the argument, Sam may most reflect the theme of act in haste, repent at leisure as he lost everything he most cherished through a quarrel. Otherwise, Sam may most reflect the theme of longsuffering and unrequited love. He never relinquished his love for nor dream of happiness with Sophy; he held on till her final march through town.
The name "Twycott" was most likely made up by Hardy by combining a form of "two" with the Old English surname "Cott," which was used to denote a hard, unfeeling person: twy + cott. Randolph was the other "twy" "Cott." Twycott may most reflect the theme of the folly of hard-hearted lack of concern for another person's feelings and interests. It would be hard to apply this to his decision to marry her, but it may certainly be applied to how he treated her thereafter and how he permitted Randolph to treat her.
Randolph may most reflect the theme of folly in leaving a son's inner character unchecked, unmolded and disciplined. Because Randolph's will and baser impulses were never checked by the other half of the Twy + Cott duo, he drained Sophy of every small joy of motherhood, then of every hope of joy in widowhood. To seal his actions, he rode like an unhooded executioner in the most prominent place of her funeral train.
There are several themes Thomas Hardy develops through different characters in “The Son’s Veto”. Sophy develops the theme of selflessness and sacrifice when we see her sacrificing her happiness with the only one man she loved, Sam, for the sake of her son. Sophy heeded to her son’s, refusal of her union with Sam. According to her son, Sam was not “gentleman” enough to marry his mother. He was an uneducated man from her mom’s past.
Sophy also developed the theme of loneliness as we see her dwindle with loneliness and misery till she dies. All the characters develop the theme of fate as we see each of ending up how they did due to the decisions they made.
Sophy also develops the theme of role of women in the 19th century where we see women having no say in their lives. It’s purely determined by the men.
Sam and Sophie develop the theme of love and romance. We meet them in the very beginning as two young love birds and we also see them meeting again after her husband’s death and the romance and love can still be felt.
Mr Twycott and his son Randolph develop the theme of social class, male chauvinism and the role of men in the 19th century as we see both of them being class conscious, Mr. Twycott, who was an educated financially stable priest, had to leave Gaymead unceremoniously because marrying Sophy, his maid, would have been committing “social suicide”.
Randolph, being a priest, develops the theme of religious hypocrisy since he prohibits his mother from marrying Sam based on his social class which is contrary to the Christian faith where love is the one thing that he should have been advocating for. Also being a priest, he expresses his disgust for Sam based on social class difference which is just hypocritical and an irony of his faith.