What was Randolph's reaction at the end of Hardy's story "A Son's Veto" when his mother dies?
[S]he seemed to be pining her heart away. 'Why mayn't I say to Sam that I'll marry him? Why mayn't I?'....
Some four years after this date a middle-aged man was standing at ... [his ] fruiterer's shop ... from the mourning coach a young smooth-shaven priest in a high waistcoat looked black as a cloud at the shop keeper standing there.
Your question is a little ambiguous as you don't specify Randolph's react to what when his mother dies: to her death; to his triumph over his mother; to Sam; to have carried his point in what was due to himself and his father? As the above quote from the end of the story shows, there is no indication of Randolph's reaction to his mother's death. All we are told about is his (1) appearance on the last ride with her coffin and his (2) attitude toward Sam Hobson. To know any more, we must infer his reactions from what is in the text.
Starting with Randolph's reaction to Sam, he rode past Sam and "looked black as a cloud at the shop keeper standing there." This suggests that Randolph really felt justified in his refusal to accept or permit his mother's love for or marriage to Sam. It seems that even after Sophy's death, the village simplicity that Randolph repressed and loathed in his own mother and in Sam governs him so completely that he must express that loathing to innocent, downcast mourning Sam as he drives by. Randolph seems to be escorting Sophy as though she were a prisoner on her way to the guillotine even while she is in the freedom afforded by death. Randolph seems to want to dominate even that freedom so as to keep her separate from Sam.
As to Randolph's reaction to Sophy's death, we can only infer from the few brief words of text that we have what that reaction might have been. We know that (1) he is "smooth-shaven" in an era when it was not unusual for men to go days without shaving; (2) he is dressed stiffly and rigidly in a "high waistcoat"; (3) he is not so moved by grief and sorrow that he either keeps to himself or grants a generous look of pity upon another mourner; (4) he looks "black as a cloud" at Sam standing at the side of the road, hat in hand.
From this we might infer that his reaction to Sophy's death is a cold-hearted one. His reaction does not soften his cold heart, nor does it make him repent or think differently of his restrictive behavior toward Sophy. His reaction seems to be focused more upon the appearance he gives as a unbending young priest than upon grief for his loss: "a young smooth-shaven priest in a high waistcoat looked black as a cloud ...." One might even wonder if he might think of Sophy's death as her just deserts and a vindication of his own demands.
At ghe end, Hardy shows that Sophy is still dominated by her own son. He doesn't feel guilty in any way and still sees everything from his own biased perspective. he doesn't realise all that he has done to his mother.
He is wearing black; the color black dominates and over-shadows all other colors just as he has over-shadowed Sophy.
Hardy shows, in a way, how religion was abused since she showed Randolph as a priest. Randolph still possessed his mother in her death like he possessed her before. He feels justified still in all the decisions he took as her son.
At the end of the story, Randolph, when his mother died, was in a coach that was going to the funeral procession, and he was staring at Sam looking "Black as a cloud", which we hope means that he was in despair and he was probably realising what he had done by not allowing her to marry the man she loved, but really he is still hating Sam.
Sophy had lived a lonely life after the death of her husband and her son wouldn't let her marry Sam, who was of lower class, claiming that if she did, his reputation will destroy and because she loved her son a lot, she didn't marry him and gave up her happiniess for his.
So we hope maybe after her death, Randolph started feeling guilty, seeing Sam and knowing that her life would have been happier with him in it, but Randolph is proud of being a clergyman and still thinkshe is right.