Detestable is a very strong word, even for Randolph. The synonyms of "detestable" are abhor, abominate, loath, hate. These describe appropriate reactions toward a mass murderer, but not toward Randolph. What is certain, though, is that Hardy does a good job of making us dislike Randolph and completely disapprove of his behavior. Hardy takes care to make Randolph an unsympathetic character right from the beginning. The first words Randolph utters are:
'Has, dear mother--not have!' exclaimed the public-school boy, with an impatient fastidiousness that was almost harsh. 'Surely you know that by this time!'
We are not apt to forgive him this verbal temper tantrum after the narrator's description of Sophy and especially after the narrator's comment that she could retaliate against him for his unkindness by telling "him to wipe that crumby mouth of his ..." as he is nibbling cake hidden in his pocket. We are drawn further into an unforgiving opinion of Randolph when we learn more directly of his opinion of his mother:
[her son] was now old enough to perceive these deficiencies [of education] in his mother, and not only to see them but to feel irritated at their existence.
It is clear the narrator gives us no reason to love Randolph and that this negativity is confirmed and exploded into shock and disdain when he responds to his mother's announcement that she would like to remarry, granted, to remarry a man who is not a well-bred, aristocratic "gentleman" who accords with Randolph's school-boy standards:
He hoped his stepfather would be a gentleman? [Randolph] said.
'Not what you call a gentleman,' [Sophy] answered timidly. ... The youth's face remained fixed for a moment; then he flushed, leant on the table, and burst into passionate tears. ... 'It will ruin me! A miserable boor! ... a clown! It will degrade me in the eyes of all the gentlemen of England!'
Later, when he has "a more manly anger," Randolph is even more hard-hearted and unfeeling in keeping with the symbolism of his surname: "Cott," an English nickname given to people who were hard-hearted and unfeeling. (An ironic contrast is Randolph, which means "wolf shield" and symbolizes guardianship, loyalty and a protector. Ironically, Sophy named Randolph to be her loyal protector.)
When Sophy represents her desire to marry Sam to Randolph after he has entered college and become basically independent of her, Randolph calls upon his father's honor and makes Sophy swear not to wed ungentlemanly Sam:
taking her before a little cross and altar ... [he] bade her kneel, and swear that she would not wed Samuel Hobson without his consent. 'I owe this to my father!' he said.
While we have no reason for feeling anything positive toward Randolph, Hardy blames it mostly upon his father's pride ("Mr. Twycott knew ... he had committed social suicide") and upon Randolph's "excellent" education:
his education had by this time sufficiently ousted his humanity to keep him quite firm[against [Sophy]; though his mother might have led an idyllic life with her faithful fruiterer ....
Hardy even excuses Randolph's behavior on two counts, confirming "detestable" is too strong a word. The first is his given name, Randolph; Sophy wished for a loyal protector. The second is the description of Randolph's early years and sympathies:
his wide infantine sympathies, extending as far as to the sun and moon themselves, with which he, ... had been born, and which his mother, ... had loved in him; ....