JOHANNESBURG, South Africa (AP) _ The United Democratic Front, the nation's largest anti-apartheid coalition, marked its third birthday today with a vow to intensify its push for change despite the government's emergency restrictions.

In another development, a 32-year-old white woman died of injuries suffered when a landmine blew up her car as she and her three children were returning home from church Sunday near Nelspruit in Transvaal province.

One of Marietjie Roos' children, an 8-year-old boy, underwent a second brain operation today at a Pretoria hospital and was in critical condition. The two other children were slightly hurt.

About 1,000 people, most of them students, marked the United Democratic Front's anniversary at a noisy indoor rally at the University of the Witwatersrand in Johannesburg. But police banned another coalition meeting that was to take place at city hall in Cape Town.

The Progressive Federal Party, which represents the anti-apartheid opposition in the white chamber of Parliament, said today the government's list of 8,551 state-of-emergency detainees omitted the names of at least 2,500 people held since the emergency declaration June 12.

The party said the government reported only the names of those people who have been detained for more than 30 days.

By law and custom, apartheid establishes a racially segregated society in which South Africa's 24-million black majority has no vote in national affairs. The 5-million white minority controls the economy and maintains separate districts, schools and health services.

Under the state of emergency, press regulations are in effect that prohibit the publication of the names of detainees without official confirmation. The measures also ban the reporting of security force activities without permission and the publishing of what the government considers ''subversive statements.''

The government has said it imposed the state of emergency in an effort to stop unrest related to apartheid.

Also today, Finance Minister Barend Du Plessis announced the government would spend $1.24 million to assist the families of people detained under the state of emergency. He said $1.2 million would be allocated to rebuild policemen's homes destroyed in the unrest.

The government's Bureau for Information reported today a black man was killed overnight by security forces trying to disperse a crowd of about 100 blacks who set fire to a house in Klein Skool, a township near Port Elizabeth.

About 245 people have been killed in unrest since the emergency was declared.

The government has blamed the outlawed African National Congress guerrilla movement for the landmine explosion that killed Mrs. Roos, but the ANC has not commented.

The multiracial United Democratic Front, which claims more than 2 million members, decided not to stage any major events to mark the anniversary of its founding, in part because of a ban on unauthorized public gatherings under the state of emergency.

''But all over the country, thousands of our supporters will solemnly be observing in various ways this occasion when three years ago about 15,000 South Africans descended on Mitchells Plain (near Cape Town) to launch the UDF,'' the front's national publicity secretary, Murphy Morobe, said in a statement.

Dozens of the United Democratic Front leaders, and thousands of members of its affiliated organizations, are among those detained without charge under the emergency regulations.

However, Morobe said the United Democratic Front ''has not only survived the most severe state repression but has grown into a powerful mass movement. One would have to gag a whole nation to crush the UDF today.''

''Two months into this national state of emergency, the UDF refuses to throw in the towel,'' he said. ''Rather than submit to state repression, we've chosen this moment to intensify our activity.''

Also today, an organizer of Desmond Tutu's installation as Anglican archibishop of Cape Town released the list of people who have been invited to the Sept. 7 ceremony.

Terry Crawford-Browne said among the 122 Americans on the list are singer Stevie Wonder, actor Bill Cosby, Sen. Edward M. Kennedy, Mayor Coleman Young of Detroit, former U.N. Ambassador Andrew Young, and Coretta Scott King, widow of civil rights leader the Rev. Martin Luther King Jr.

Tutu is the bishop of Johannesburg, winner of the 1984 Nobel Peace Prize and an outspoken black critic of apartheid.