"The Helping Hand", a 1950 novelette by Poul Anderson; the full text is available here. The story was first published in Astounding Science Fiction, May 1950, available at the Internet Archive.
A planetary ambassador whose planet is considering joining a federation deliberately insults the entrance committee so that his planet is denied entry;
Not a federation, but a postwar aid program:
When terrestrial technology came to Skontar and Cundaloa, its first result had been to unify both planets—ultimately—both systems into rival states which turned desirous eyes on the green new planets of Allan. Both had had colonies there, clashes had followed, ultimately the hideous five years' war which had wasted both systems and ended in a peace negotiated with terrestrial help. It had been simply another conflict of rival imperialisms, such as had been common enough in human history before the Great Peace and the formation of the Commonwealth. The terms of the treaty were as fair as possible, and both systems were exhausted. They would keep the peace now, especially when both were eagerly looking for Solarian help to rebuild.
[. . . .]
The aid program was still no more than a proposal. The Assembly would have to make a law detailing who should be helped, and how and how much, and then the law would have to be embodied in treaties with the planets concerned. The initial informal meeting here was only the first step. But—crucial.
deliberately insults the entrance committee
The representative of Skontar arrives late for the meeting . . .
"You are late," said one of the ministers with thin politeness. "I trust you were not detained by any difficulties."
"No, I underestimated the time needed to get here," answered Skorrogan. "Please to excuse me." He did not sound at all sorry, but lowered his great bulk into the nearest chair and opened his portfolio. "We have business now, my sirs?"
. . . and continues to act rudely:
"And, of course, some question of military resources will arise—" began the Chief of Staff.
"Skontar have own army," snapped Skorrogan. "No need of talk there yet."
"Perhaps not," agreed the Minister of Finance mildly. He took out a cigarette and lit it.
"Please, sir!" For a moment Skorrogan's voice rose to a bull roar. "No smoke. You know Skontarans allergic to tobacco—"
"Sorry!" The Minister of Finance stubbed out the cylinder. His hand shook a little and he glared at the envoy. There had been little need for concern, the air-conditioning system swept the smoke away at once. And in any case—you don't shout at a cabinet minister. Especially when you come to ask him for help—
so that his planet is denied entry;
This time the silence lasted a long while. And Dalton realized, with a sudden feeling almost of physical illness, that Skorrogan had damaged his own position beyond repair. Even if he suddenly woke up to what he was doing and tried to make amends—and who ever heard of a Skontaran noble apologizing for anything—it was too late. Too many millions of people, watching their telescreens, had seen his unpardonable arrogance. Too many important men, the leaders of Sol, were sitting in the same room with him, looking into his contemptuous eyes and smelling the sharp stink of unhuman sweat.
There would be no aid to Skontar.
returns home in disgrace;
They were waiting near the bottom of the gangway, the high chiefs of Skontar. Under an impassive exterior, Skorrogan's belly muscles tightened. There might be death waiting for him in that silent, sullen group of men. Surely disgrace—and he couldn't answer—
lives in disgrace
"I cannot strip you of your hereditary titles and holdings," said the Valtam. "But your position in the imperial government is ended, and you are no longer to come to court or to any official function. Nor do I think you will have many friends left."
"Perhaps not," said Skorrogan. "I did what I did, and even if I could explain further, I would not after these insults. But if you ask my advice for the future of Skontar—"
"I don't," said the Valtam. "You have done enough harm already."
". . . then consider three things." Skorrogan lifted his spear and pointed toward the remote glittering stars. "First, those suns out there. Second, certain new scientific and technological developments here at home—such as Dyrin's work on semantics. And last—look about you. Look at the houses your fathers built, look at the clothes you wear, listen perhaps, to the language you speak. And then come back in fifty years or so and beg my pardon!"
until he visits one of the member planets with his descendant
Not his descendant but his old friend Thordin, the Valtam (emperor) of Skontar:
"I wish you could spare me a few hours tomorrow," said Skorrogan.
"Well—I suppose so." Thordin XI, Valtam of the Empire of Skontar, nodded his thinly maned head. "Though next week would be a little more convenient."
The note of urgency could not be denied. "All right," said Thordin. "But what will be going on?"
"I'd like to take you on a little jaunt over to Cundaloa."
and they see how abased; touristy and exploited member planets are.
"You won't find significant art, literature, music here any more—just cheap imitations of Solarian products, or else an archaistic clinging to outmoded native traditions, romantic counterfeiting of the past. You won't find science that isn't essentially Solarian, you won't find machines basically different from Solarian, you'll find fewer homes every year which can be told from human houses. The old society is dead; only a few fragments remain now. The familial bond, the very basis of native culture, is gone, and marriage relations are as casual as on Earth itself. The old feeling for the land is gone. There are hardly any tribal farms left; the young men are all coming to the cities to earn a million credits. They eat the products of Solarian-type food factories, and you can only get native cuisine in a few expensive restaurants.
"There are no more handmade pots, no more handwoven cloths. They wear what the factories put out. There are no more bards chanting the old lays and making new ones. They look at the telescreen now. There are no more philosophers of the Araclean or Vranamauian schools, there are just second-rate commentaries on Aristotle versus Korzybski or the Russell theory of knowledge—"