IT SEEMED, on the whole, good news that Britain, France, Italy and the Netherlands had offered to take part in the peace force being organized by the United States to police the Sinai after the Israelis finish evacuating next April. It would give the United States some welcome company in its sponsorship of Camp David. With any luck, those taking part would end up bored to tears but in proud possession of world-class volleyball teams.

How regrettable, then, that an exercise meant to draw nations together has produced yet more friction. The trouble lies, moreover, not only between Israel and the Europeans, who wish to join the force in order to get a voice in the next stage of Mideast diplomacy and to join in a way that will let them demonstrate their rejection of Camp David to their Arab oil suppliers. There is also a disagreement between Israel and the United States, which wants the Israelis to stop grumbling about the Europeans' verbal formulations and to accept the modest benefits of actual European participation in the force.

The dust has not yet settled from the AWACS controversy and from Mr. Reagan's remarks on the Saudi peace plan--that plan, by the way, is itself now under a dark new cloud of uncertainty as a result of the abrupt shattering of the Arab summit called to promote it. But the Israeli foreign minister has hastened here to untangle the Sinai issue. Meanwhile, American-Israeli plans for strategic cooperation are coming into public dispute.

Some of the trouble between these two friendly and supposedly like-minded countries is not of their making. The Europeans' effort to have their cake and eat it, too, on the peace force, for instance, is shabby, advertising their unreliability as much as their civic-mindedness. On the future of the Palestinians there are many questions, but the peace between Egypt and Israel is here and now. It would be nice to have allies unashamed to support the single part of any Mideast peace process that 1) exists and 2) works.

But much of the strain between the United States and Israel is of their own making. President Reagan has yet to find an effective way to manage this uniquely complex relationship. The handles to its separate parts seem to be scattered among subordinates insensitive to the requirements of coordination and tact. Often, when Mr. Reagan himself joins in, he leaves people asking whether he understands what has gone before. On his part, Prime Minister Begin has chosen to treat each issue that comes along as a do-or-die test of American fidelity. He seems intent on compelling the United States to choose between its Israeli interests and its Arab interests, when the basic American policy is to try to pursue them both.

No manner of conducting relations can erase the real differences that lie between the United States and Israel. This is all the more reason to keep extraneous differences from clogging the machinery. Cool heads at the bureaucratic level can help, but no substantial improvement can be expected if the matter is not addressed at the top.