The similar theme ("central idea") in Hardy's "The Son's Veto" and Pritchett's "The Fly in the Ointment" is parent-child relationships.
In "The Son's Veto," Sophy (widow of Vicar Twycott, and mother to Randolph) is a country girl who married above her station. Never able to master "upper-class" English, she is ever an embarrassment to her son. As he grows up, he becomes oppressively controlling. Years after she has been widowed, she approaches the idea of returning home and marrying a man she knew in her youth. The selfish Randolph forbids it:
The youth's face remained fixed for a moment; then he flushed, leant on the table, and burst into passionate tears.
Randolph then storms off to another room:
It was long before he would reply, and when he did it was to say sternly at her from within: 'I am ashamed of you! It will ruin me! A miserable boor! a churl! a clown! It will degrade me in the eyes of all the gentlemen of England!'
And so, Sophy puts her desire aside—revisiting it occasionally for four or five more years, believing that as her son matures, he will care little about what she does. The selfish son's answer is always the same, until he eventually forces Sophy to promise ("vow") that she will never think of marrying Sam without her son's approval—he might as well have imprisoned her.
...finally taking her before a little cross and altar that he had erected in his bedroom for his private devotions, there bade her kneel, and swear that she would not wed Samuel Hobson without his consent.
The consent is never given; soon Sophy dies.
In "The Fly in the Ointment," the father is the stronger figure. The son comes to visit his father as the older man closes the doors on his business because of a serious financial crisis in the business world. The son comes to lend his father moral support; we find that the father has no love for his son:
"Come in, Professor," said the father. This was an old family joke. He despised his son, who was, in fact, not a professor but a poorly paid lecturer at a provincial university.
The father knows how little his son is paid: he has no respect for the young man because of this! It is relatively easy to see that money means everything to this father. In light of this, the son says he wishes he could help—but all his father hears is "cash."
"What I came around about is this," said the son awkwardly and dryly. "I'm not rich. None of us is...we can't do anything. I wish I could, but I can't...but the idea of your being—you know, well short of some immediate necessity, I mean—well, if it is ever a question of—well, to be frank, cash, I'd raise it somehow."
The father's "little face [was] like a fox"...an animal often personified as sneaky and unscrupulous. He immediately wants to know why the son never said anything, demanding details about the non-existent money.
In both stories, we see poor parent-child relationships. In both stories, one member of the family is accommodating and cooperative. The remaining member has no regard for the other at all, thinking selfishly only of himself.