Children finally traipsed back to school here this week, "a-skippin' just like they should," one grinning grandfather said, "and tired of watching 'Days of Our Lives' on TV."

That was not the only soap opera Philadelphia school children viewed almost to the edge of winter this year as they waited out a 50-day strike by the city's teachers.

They also watched a political sit-com that featured:

A City Council session that broke up in a City of Brotherly Love brawl with councilmen throwing ice water at each other, engaging in duels with the hearing stenographer's tripod and finally just decking one another.

A mayor who used a confrontation with striking teachers as a television opportunity to quote Rudyard Kipling about the virtue of keeping your head while all those around you are losing theirs, only to watch as his driver lost his and started fighting with a teacher.

Clergymen who blocked downtown traffic to get the mayor's attention and teachers who marched on Philadelphia's historic City Hall chanting: "Mayor Green, Mayor Green, the kids are saying you've been mean."

The fall season's unusual version of the Philadelphia Story ground to an intermission, but probably not a conclusion, in midweek with the teachers accepting a court order to return to school just hours before labor union leaders threatened to close down the town in a one-day general strike.

Almost no one in Philadelphia was laughing. And almost no one thought the intermission had solved anything more than getting the kids back to school for the time being, more than seven weeks late.

At the interlude, the city still faced a $236 million school-budget deficit, a tough teachers' union accustomed to winning showdowns, a beleaguered mayor whose critics think he is using the crisis to prove his political manhood, and a real-world 1981 certainty that financially troubled cities like Philadelphia have little hope of running to either state or federal governments for aid.

For Mayor William Green III, a soap-opera-handsome liberal who has spent most of his career trying to edge out of the shadow of his father, the crisis was proving to be a political watershed.

At 42, Green has been in elective politics for more than 17 years, ever since he quit law school 10 credits short of a degree to run for the congressional seat vacated by the death of his father, one of Philadelphia's legendary Democratic political bosses.

But in Philadelphia, where politics is played by the old rules, his father's old cronies still call him Wonder Boy and Little Willie the Mayor. Others call him Plastic Man, say he is short on leadership and repeat the most stinging shot of all: "I looked into his eyes and nobody was home."

Green's father was a power politician who referred to himself as "chairman of the board." He delivered Pennsylvania to John F. Kennedy at the 1960 Democratic National Convention as handily as any boss in the land.

And when Arthur Schlesinger Jr. criticized him for running politics like it was a business, he wondered what was wrong with that, and wrote off the Kennedy historian as "an Ivy League Ku Klux Klanner."

Young Green never played the game that way, and when he went to Congress in 1963 he spurned the old machine politics of his father for the image-honing of the television era that was already changing American politics.

But when he became mayor in 1979, after losing a Senate race in 1976, he walked back into a game where the old rules played better.

He also walked into a game that had been dominated for the previous eight years by the law-and-order mayor and ex-police chief, Frank Rizzo, and in which school problems had been rampant for more than a decade.

By late this summer, with another of Philadelphia's chronic school strikes inevitable, Green announced to the city: "I am prepared to lead." It was not quite that easy.

Green's proposal to raise property taxes 10 percent as part of a package to wipe out the $236 million school-budget deficit received high marks for realism from the Chamber of Commerce and some other civic leaders. But it ran into an abrupt dead end in the City Council, which staggered into the strike with fists and water flying.

"I hope the children of Philadelphia were watching cartoons and not this," Councilwoman Augusta A. Clark, chairman of the Education Committee, said through tears after the extraordinary council session.

Meanwhile, the mayor's decision to support the school board's move to lay off 3,500 teachers and roll back an already negotiated pay increase brought on the wrath of the powerful Federation of Philadelphia Teachers, which had cut its teeth on four successful strikes in the past dozen years.

"Liar, liar," the teachers chanted at Green when he insisted that Philadelphia simply didn't have the money to foot the bill for the schools.

As the strike wound on, the only person in town who seemed to be enjoying the action and Green's discomfort was Rizzo.

Rizzo reluctantly bowed in 1979 to a constitutional provision that prevented him from seeking a third consecutive term as mayor, but the law doesn't bar Rizzo from running in 1983. As Green struggled with the teachers, the pols and a lengthening strike, Rizzo confided that he was watching like "a tiger in the grass."

While the teachers marched on Green, Rizzo marched through the streets of south Philadelphia last month in an Edward O'Malley Athletic Association parade. The streets were lined with signs saying "Save Our City, Frank." And reporters duly recorded the statement of a schoolgirl who announced: "My daddy says that, besides God, Frank Rizzo is the greatest man in Philadelphia."

Green warned his staff to hunker down for a long battle, because it was "melt-down-the-mayor" time. And he sounded like he was tired of melting.

Last week's court order temporarily restored the 3,500 teaching jobs that Green said had to go, averted a general strike and sent the teachers and the children back to school for the time being. But it didn't provide the money to end a $236 million school-budget deficit, leaving the political soap opera unfinished.