Let us hope that it is easier to achieve peace between the British and the Argentines than it is between our secretary of state and our ambassador to the United Nations, who have fallen out over the Falklands.

And let us further hope that Jeane J. Kirkpatrick does not speak to Third World countries the way she did to Alexander M. Haig Jr., as reported in gripping detail in the current issue of Newsweek. The 45-minute exchange was nuclear in nature. The Federal Communications Commission may have to step in and forbid them the use of the telephone lines if they ever fall to discussing the Falklands again. Had they been in the same room, ashtrays would have been hurled.

The tousle-headed, strong-minded ambassador showed up at the White House on Memorial Day to tell President Reagan her side of the story. She was asked by reporters, as she strode out of the West Wing, about her chat with Haig.

"I have many long conversations with the secretary," she rapped out with her wonted crispness.

Kirkpatrick is not the first U.N. ambassador to have her own foreign policy. Andrew Young springs to mind as a unilateralist, who made approaches to the Palestine Liberation Organization without going through the tedium of checking with his nominal superiors at the Carter State Department. That bit of enterprise cost him his job.

Whether either Haig or Kirkpatrick has threatened to resign--"either he (she) goes or I do"--over their differences in policy is not known. Both have used the resignation option rather liberally. Haig hinted he would quit even before he was confirmed. Kirkpatrick came within an ace of packing it in over Poland, because she found the Reagan response to martial law unacceptably wimpy.

The timing of the spat is unfortunate for the administration, which has lately been preening itself on a new order and unity in foreign policy. It was not the only awkwardness of the holiday weekend. On the eve of Reagan's trip to Europe, where he hopes to be seen as a rational, serene, peace-seeking world leader, The New York Times published one of those scary Pentagon scenarios which shows the Defense Department planning for a "protracted" nuclear war.

Kirkpatrick is a personal favorite of the president's, which Haig is not. Reagan was smitten by her articulate presentation of the position that authoritarian governments are better than totalitarian governments. She has yet to meet a Latin-American dictator she didn't like and is especially partial to Argentina's Gen. Leopoldo Galtieri. She is the principal architect of our Latin-American policy of befriending his ilk. The fact that it may die in the fighting is the only good thing that some people see in the bloody war.

She demonstrated her sympathies by attending, on the night of the invasion, a dinner given in her honor by the Argentine ambassador. She explained on television that the date had been set at her convenience. She justified the invasion by saying that it was "not a military aggression" but an "armed action" undertaken by a country which thinks it owns the Falklands.

After a month of neutrality, the president was won over to the side that Americans had taken instantly. The secretary, whose initial enthusiasm for Buenos Aires was eroded by close encounters during his shuttle negotiations, took issue with Kirkpatrick for continuing to hold hands with junta representatives.

While someone, probably at his end of the line, took it down, Haig accused her of being "mentally and emotionally incapable of thinking clearly about the Falklands because of your close links to Latins."

Kirkpatrick fired back that he was "incapable of understanding Latin-American sensibilities." Besides she said, snippily, she works "for the president not the secretary of state."

Haig and his aides, she raged, are "amateurs" and "Brits in American clothing" and "totally insensitive to Latin cultures."

One of them probably should have hung up right then, because what followed shows that Kirkpatrick has not mastered the niceties of diplomatic language. Haig's people are "totally unrealistic" to "think the Latins will come whoring after us because they are right-wing juntas and right-wing juntas don't rest well in beds with Communists."

In her final, disembowelling thrust, she asked, "Why not just disband the State Department and have the British Foreign Office make our policy?"

Kirkpatrick's misplaced tenderness for thin-skinned Latin thugs is well known. Her reference to their "sensibilities" is grotesque in the Falklands context. Take the case of the Navy Captain Alfredo Astiz, who was picked up by the British on one of the islands. He is known to be the torturer-in-chief of the regime, and suspected of having two French nuns dropped from a helicopter.

Haig is not the easiest man in Washington to work for. But Kirkpatrick is going to have him come off as St. Francis of Assisi if she doesn't watch her words.