One of the most poignant scenes in last year's NFL players strike came at an informal Redskins practice on a playground in Reston. Tony Peters stood on the sidelines entertaining his 3-year-old son while his teammates worked out.

"Sometimes I miss the daily schedule," Peters had said, smiling, as his son Tony Jr. tugged on his pants and asked to go home. "This time of year, I'm not used to baby-sitting. I'm used to playing."

Peters spent most of the players strike baby-sitting his four children. When the season finally was resumed, he completed his best year in pro football. He made the Pro Bowl for the first time, then he signed a four-year, $1 million contract in the offseason that he said provided financial security for the rest of his life. He has played eight years in the National Football League, four with Cleveland and four with Washington.

"He's an easygoing, nice man with a fine sense of humor," said attorney Richard Bennett, who negotiated the contract for Peters. "He is always talking about his family. He has a close sense of identity with his family."

Bennett said he was stunned yesterday when he heard that Peters had been arrested and charged with conspiracy to possess and distribute cocaine. "I can't believe it," he said.

Peters is one of the Redskins stars, a well-liked team leader. He was a major reason why Washington changed from a defensive also-ran to one of the league's best units last season.

On the field, he has a nasty way of tackling with authority; off the field, he is a gentle man who rarely projects anything close to a macho image.

"I don't know anyone on the team who is respected more," safety Mark Murphy once said about Peters. "Everyone knows he plays hard and is prepared. That's all you can ask for from a teammate."

Peters also has great pride. He candidly admitted that he had a poor 1981 season, and was partly responsible for the Redskins' mediocre performance. "I had gotten lackadaisical and I wanted to make a change," he said late last season.

He stopped taking what Defensive Coodinator Richie Petitbon called "vacations" during games. It was Petitbon who decided, during the 1980 season, to bench longtime all-pro Ken Houston and replace him with Peters. It was a controversial choice that put pressure on Peters, although he claimed, "I never tried to replace Ken Houston, because you can't do that, but I wanted to play better for Tony Peters and for this team. I knew I could give them more than I had . . . I should be entering the peak years of my career. I didn't want to let them go by."

Last season, Peters increased his aggressiveness and his concentration. The better he played, the better the defense in general and the secondary, in particular, played. There was no better strong safety in the NFL by the end of the year.

Peters has a quiet confidence that developed, he said, during his days at the University of Oklahoma, when he was a teammate of fellow Redskin Joe Washington. When he did not like decisions being made by the players union leadership last fall, Peters spoke out in opposition. When he disagreed with coaching decisions or offensive execution, he never hesitated to criticize.

"It's not a matter of needing money," he said. "I just don't know if we are staying out for the right reasons. I can survive as long as I have to . . . I was going crazy. The thing is, we could have accomplished all this weeks ago."

Peters, 30, was born in Paul's Valley, Okla., in a family with 10 brothers and sisters. He attended Northeastern Oklahoma, then transferred to Oklahoma, where he was all-Big Eight and a member of the Sooners' 1974 unbeaten team. Since joining the Redskins, he has received his real estate license.

"I've never been happier," he said when he was named to the NFC Pro Bowl team. "This is my most satisfying accomplishment. I was tired of being a loser."