Sitting on a bench in the inadequate shade of a tree in Dumbarton Oaks, Beatrice Brademas, the Indiana congressman's 76-year-old mother, fanned herself with a palmetto. Mrs. Brademas was highly pleased that after 50 years of existence her son, John, had finally gotten married. She was so pleased, in fact, that she dashed back from Greece, which is where she'd been vacationing, to attend yesterday's reception at Dumbarton Oaks.

"I don't know why John's never married before. I really don't," she said thoughtfully. "Now he's never said this to me, but I think that maybe when he saw how many divorces there were in Congress - that might have deterred him." She giggled impishly, then said, "It overwhelmed the people back home. Because they didn't think he'd EVER get married, I used to tell them, 'He's already married to the Third District of Indiana.' Because, you know, he works an 18-hour day, I don't know how Mary Ellen will like that."

Well, it remains to be seen how the former mary Ellen Briggs, now a medical student at Georgetown, will, in fact, like that. Let's just say that yesterday the divorced mother of four who married the Majority Whip in early July got a fair idea of what was in store for her. For hours she stood in the beastly heat on a receiving line with her husband and House Speaker Tip O'Neill greeting people like Vice President Walter Mondale and Joan Mondale. Transportation Secretary Brock Adams, HEW chief Joe Califano, Rep. Shirley Chisholm, Ambassadors Peter Jay and Simcha Dinitz - along with hundreds of others. And tried to remember everyone's name.

Dumbarton Oaks is not, of course, the simplest little spot in the city to hold your wedding reception or bar mitzvah, or what-have-you. Matter of fact, Brademas caused quite a stir when he turned out to be the only party - aside from Mr. and Mrs. Robert Woods Bliss who, after all, donated the place to Harvard - allowed his own shindig on the premises. But then he used to be what is called a Harvard overseer.

"I don't know what that is," said his new wife, "Yes, it does sound like somebody with a whip, doesn't it? Most appropriate."

"It's the same as a trustee," explained Brademas.

And Tip O'Neill, who sponsored the afternoon reception said, "There was no problem (with Harvard whatsoever. As soon as they heard about John getting married, they said - 'NOW we have a use for that.'" He laughed jovially, throwing an arm around Brademas. "Yes, they said, 'We had that famous conference - now what can we do to equal that?' Right John?"

That famous conference occurred in 1944 and ultimately led to something that became known as the United Nations. Yesterday's little gathering of about 600 was perhaps less portentous than the earlier one, but a whole lot more romantic. A seven-piece brass band that played stolid 19th-century music; strawberries in champagne; and "people" sculpture benches in the garden where Shirley Chisholm sat with Arthur Hardwick Jr., a Williamsville, N.Y., architectural designer who became her fiance on July 4.

"The maintenance on a place like this . . ." she murmured to him.

"Yes," he said softly. "There's no way to possibly even estimate the taxes on a place like this."

They will be married, he says, before the year is out.

Joan Mondale breezed through, exclaiming how "neat" it was to be a Vice President's wife. "It really is neat. And I'm getting recognized all over," she said. "Where was it - someone said 'Oh hello, Mrs. Mondale?' Oh yes, the post office. And I've never had so many press before. It's very, very flattering. Thirty-four press people when I was in San Antonio last week. Can you IMAGINE?"

And over in another corner of the party was Israeli Ambassador Dinitz, who said, consolingly, "We shouldn't really get despondent when points of disagreement arise . . . Our areas in common (between the U.S. and Israel) are much greater than our differences. If there were no points of disagreement, my job would be obsolete."

Later he was joined by a small man in white shoes - Joseph Hirshhorn of museum fame, who told the ambassador, "You don't know this. But I set up a $75,000 art fund in Israel."

The ambassador seemed to know that.

"And who do they give it to?" Hirshhorn continued, naming a famous Israeli artist, "Him. He needs it like a hole in the wall. They should have given it to an unknown. But him -"

At this point he accepted a glass of champagne, toasting the ambassador with, "I'chaim." A waiter came by with hors d'oeuvres. Holding the ham aloft for inspection. Hirshhorn informed the Israeli ambassador, "I want you to know this is kosher." And then he swallowed it all.