New Delhi — In the end, it could be a tale of two women, intent on avoiding an open and embarrassing split, at the biennial meeting of the Commonwealth heads of government, which opens in New Delhi on Wednesday. This could prove the least harmonious of 23 such meetings in the post-World War II years.
It will require all of the skills of the chairman, Indira Gandhi, and British Prime Minister Margaret Thatcher to heal deep wounds among the Commonwealth's 48 members on the United States invasion of Grenada - a Commonwealth member-state.
There are also sharp divisions on the lack of progress in gaining independence for South African-controlled Namibia and the ticklish issue of a new world monetary order, a move which both the US and Britain oppose.
Yet the most difficult task could be soothing tempers among Caribbean leaders , six of whose armies, in a fashion, swept across Grenada's beaches, under US command. They will be here in New Delhi, viewed by many as little more than Washington's surrogates. And they could become the fulcrum for the body's more radical states to use the six-day meeting to criticize the US.
Such condemnation could find expression in nearly all issues to be discussed - from disarmament to cruise missiles in Europe; ''demilitarization'' of the Indian Ocean; and the declaration of independence by Cyprus's minority Turks. Cyprus is also a Commonwealth member, but the organization has had little impact on the divided island since the 1974 Turkish invasion.
But it is Grenada and, more important, the state of the Commonwealth in its aftermath, that is bound to be foremost in everybody's mind.
The possible dispatch of a Commonwealth force to police the island, assuming the US withdraws, has in itself caused perceptible strains in the group.
Mrs. Gandhi is against it. Mrs. Thatcher will consider it ''sympathetically'' if its mission is clearly defined. Canada, New Zealand, and Trinidad, among others, have said they are ready to take part.
Yet it opens an unsettling specter for a number of member-states on the implications of what could become a permanent, Commonwealth ''preventive peacekeep-ing'' role in the wake not only of Grenada but also the Falkland Islands, and the demands of some of the body's tiny nations for some kind of Commonwealth arrangement to protect them.
Such a one-time force for Grenada, its proponents will argue this week, would have the advantage of removing the troubled island from superpower politics, and returning it to a familiar umbrella, even though, at the time of the invasion, that umbrella was caught nearly unawares.
For it is an umbrella that has become somewhat tattered over time. No longer is there the homogenous grouping presided over by Queen Victoria nearly a century ago, and which passed from empire to Commonwealth in 1944. Made up of former British colonies, it is perhaps one of the world's most heterogenous, international groups, ranging from vast India to 26 ''micro'' nations. Such eclecticism has led critics to charge that the body, representing Conservatives and Marxists, North and South, are held together by love of Queen and cricket, but, perhaps, by little else.
Yet, it has survived longer than any other international body in modern history, perhaps, due in large measure, to its sheer informality.
All leaders are accorded individual audiences by Queen Elizabeth II, who is head of the Commonwealth, although during its sessions she plays only a discreet role behind the scenes. Yet she is bound to voice her disapproval of a foreign power simply walking into a member state, and, perhaps as she did at the 1979 Lusaka conference, where independence talks for Rhodesia got under way, she may use her position as figurehead to build additional bridges in New Delhi this week.