The AFL-CIO's annual winter beachfront retreat opened with an unusual and symbolic event. A group of national labor union presidents committed what many here consider a cardinal sin: They crossed a union picket line to attend a seaside Sunday brunch.

With harsh words and a few obscenities, three AFL-CIO vice presidents and several other union officials went to a brunch sponsored by Hyatt Hotels Corp. despite pleas from a fellow AFL-CIO union that accused Hyatt of antiunion activities at a New Orleans hotel.

The battle of the brunch was definitely a minor event in the history of organized labor, but it captured the essence of a chronic problem facing unions. They are sometimes so busy fighting among themselves that they cannot unite to deal with larger problems such as the erosion of workers' wages, benefits and job security.

At their week-long meeting, executives of the 13-million-member AFL-CIO took several steps toward remedying such problems. The 35 leaders of the labor federation created a system of "umpires" to resolve costly organizing disputes among 96 unions, approved a plan to attract new members by offering workers low-interest MasterCards, and crafted a new multiunion team approach to organizing work places such as Blue Cross/Blue Shield.

Several unions showed off recent successes: The teachers have signed up 1,000 new "associate" members in Texas through an innovative direct-mail drive; the bricklayers have begun a novel campaign to promote their craft; the food and commercial workers have added 71,000 new members.

Their accomplishments, however, are overshadowed at times by family squabbling in the house of labor, such as the controversy over the Hormel meatpacking strike, in which a local union and its parent national union nastily attacked each other at competing news conferences.

At the 650-room Sheraton they have used here for decades, the labor chieftains often face criticism for going to a beach resort while most of their union members are shivering back north, trying to earn a living.

Contrary to the cynics' view, the labor leaders spend a good deal of time indoors. Working. Their agenda includes economic and social policy statements, political strategies, publicity campaigns, seminars, anti-Reagan tirades, some golf and day-ending expense-account dinners at one of many overpriced Collins Avenue hangouts.

The Hormel strike in Austin, Minn., was Topic A here in shouting matches and position papers. But there also were moans about two competing Sunday brunches.

Hyatt, a mostly unionized hotel chain, throws a brunch here every year for AFL-CIO brass. This year, however, the 750,000-member Service Employes International Union (SEIU) is pushing a boycott of nonunion Hyatts because of the company's refusal to sign a contract at the New Orleans Hyatt Regency, despite a National Labor Relations Board complaint.

In New Orleans, 400 Hyatt workers -- mostly blacks and Hispanics getting $4 an hour -- became the first hotel workers in that city to vote for a union in more than 25 years.

But the union vote was in 1981, and five years later, Hyatt has not signed a contract, even though it agreed to do so 13 months ago, according to an NLRB ruling that the company is appealing.

Publicizing what it sees as exploitation, the SEIU produced slick leaflets saying: "If you have a conscience, you'll definitely sleep better someplace else" than Hyatt. SEIU paid for a "solidarity brunch" to replace Hyatt's, and threw up a picket line.

But interunion conflict arises because other unions, primarily the 400,000-member hotel and restaurant employes, have contracts and good relations with the Chicago-based hotel chain. So three Chicago union leaders -- Edward Hanley of the hotel union, Angelo Fosco of the laborers and Robert Georgine of the building trades -- decided to snub SEIU instead of Hyatt.

"I don't cross picket lines. But that's not a picket line. That's just harassment," Hanley said, standing at the outdoor Hyatt buffet, gesturing toward an SEIU picket line. Hanley and Georgine said they believe Hyatt is wrong in New Orleans, but said they didn't want to alienate the company because their members depend on Hyatt jobs in other cities.

That argument didn't sell with SEIU President John Sweeney, who said, "I have to let their conscience be their guide. Let's just say I wouldn't do it." Almost all union officials agreed.

Hyatt, in its defense, slipped under the hotel room doors a brunch invitation that said Hyatt supports unionism and described the New Orleans controversy as a "misunderstanding."

Inside their private meeting room, the AFL-CIO brass had an unusually passionate, spontaneous discussion Tuesday about the need for unions to become more militant. Like almost any executive, AFL-CIO President Lane Kirkland referred the matter to committee. It is the kind of issue that will come up again: Same time. Same place. Next year.