Prime Minister Pierre Elliott Trudeau holds the key to a vast storehouse of energy resources critical to this country. But in order to beat back the Quebec separatists in the referendum last Tuesday, he was obliged to promise a new charter completely revising relations between the federal government of Canada and its 10 provinces.

Now he plunges into a delicate and complicated constitutional negotiation. For the next few years Trudeau can at best listen only with half an ear to Washington's concerns.

Prime Minister Masayoshi Ohira of Japan has followed a strong pro-American foreign policy. In keeping with nudges from Washington, he has increased Japanese defense spending, asserted a stronger political role in Asia, and moved away from Russia and toward China. To solidify that line back home, he paid an almost rapturous state visit to President Carter at the White House on May 1.

But on May 16 he lost a vote of confidence in the Diet, thanks to major abstentions by his own Liberal Democratic Party. There now ensues an election apt to push the Liberal Democrats further down the road to coalition with a party to their left. No break in foreign policy impends. But henceforth Japan will not be moving smartly in response to American pressure. hTokyo will be acting at its own measured pace in response to the push and pull of Japanese domestic politics.

Anwar Sadat is probably the foreign leader who has staked most on the American connection. He visited Jimmy Carter on April 7, and the two concerted strategy for dealing with Israel against the target date -- May 26 -- set for accord on Palestinian autonomy. Back home, Sadat found that internal politics required that he not be huddling with the Israelis at the time of the deadline. He decided that on May 14 he would announce a cabinet reshuffle and call a time-out in the talks with Israel.

On May 13 Carter telephoned Sadat and persuaded him not to announce a recess in the talks. But the day after that, Sadat changed his mind again. In fact, Sadat went back on the direct appeal by Carter, the better to adjust to his domestic pressures.

Helmut Schmidt is perhaps the most pro-American leader in German history.

On March 4 he came to Washington to confer with Carter on joint strategy for dealing with the Soviet invasion of Afghanistan. Carter asked Schmidt to join in a boycott of the Moscow Olympics. Schmidt, who had expected far more serious demands, assented with alacrity, for he faces a general election in September against a Christian Democratic opposition likely to tax his Social Democratic Party with being soft on the Russians and hostile to the United States.

Back home, Schmidt found himself under pressure from his own party to solidify ties with Russia and East Germany. He elicited an invitation to visit Leonid Brezhnev in Moscow. But he decided to go in July -- after Secretary of State Edmund Muskie met with Andrei Gromyko in Vienna on May 9. By using Muskie as advance man, Schmidt could seem to be going with the blessings of the United States, and thus mollify both his own party and the opposition.

President Valery Giscard d'Estaing is up for reelection in 1981. He needs to neutralize both commnists who emphasize ties with Moscow and Gaullists who stress French leadership in Europe -- especially over Germany.

So Giscard stole a march on Schmidt. Without telling anybody, he arranged to meet with Brezhnev in Warsaw May 19.

Margaret Thatcher heads the most openly pro-American government in Europe. Her foreign secretary, Lord Carrington, has been the chief advocate of an American proposal that Japan and the Europeans join this country in imposing economic sanctions against Iran as a penalty for taking the hostages. He achieved a great success on May 18 when the Europeans, meeting in Naples, agreed to sever all contracts with Iran dating back to the seizure of the hostages on Nov. 4.

But in Parliament a powerful coalition of Tory backbenchers and the Labor opposition came together against the sanctions. They argued that the cancellation of contracts would hurt British exports and also alienate the Moslem world, thus offending precisely those most capable of extricating the hostages. To hold her majority, Thatcher had to agree to cancel contracts only beginning now -- not as of Nov. 4.

Running through all these cases is a common theme -- disarray among friends and allies. Some see only the workings of the usual strains. Others imagine just a sharpening of economic rivalries.

My own sense is that the trouble runs deeper. For a variety of reasons, the management of allied relations has become intrinsically more difficult. The fragmented and self-serving set of objectives offered to the world by the Carter administration does not engage any friends, and causes some to scurry for cover. So until this country presents a coherent vision of the future, the alliance structure will continue to unravel -- perhaps to the point of disintegration.