Somewhere between the hours of 2 a.m. - when the last gentle sound of Johnny Rotten fades in the 13-year-old's room - and 5 a.m. - when the 10-year-old family gymnast gets up to jog outside the bedroom door - a parent in an insomniac haze ponders, "Is there life after school?"

As one woman screamed with hysteria-tinged voice, "The months of June and July should be wiped off the calendar!" Not only is she a successful mother of two young children, she is also a psychiatric social worker who counsels families. She has, however, just come up for air after a few weeks of The Summer Syndrome.

"There is a certain trauma," she blurts, ever so grateful to be able to confide in someone for a change. "Summer with the kids home is a life cycle crisis, you know, like when you get married or have children or go to college or become toilet-trained or whatever. It is very difficult . . ."

Some family care experts feel the trauma of coping with a summer full of children has increased in a world of rising divorces and two-parent careers and grandparents living cross-country and camps costing as much as private schools. When children are sprung for summer, a life style that had been hanging by a thread no longer hangs.

It is no just the logistics, the schlepping, the plotting, the decisions about camps, the hassles about summer jobs. Those interlocking schedules ("You drop the kids . . . I'll pick them up after work") - which always includes SCHOOL from 9 to 3 as the center of the universe - disintegrate, and galloping guilts are easily activated. Perfectly sane parents, given to whimsy on occasion during the school year, mutter with dead seriousness about lack of The Quality of Life in their households.

Not to worry, says one reassuring voice from shrinkdom. If anything, says Dr. Michael Kerr of the Georgetown University Family Center, today's children could use a little apartness. "Parents are dedicated; wound up in their kids. This can create a terrible dependency - and the child expects it."

You can't generalize about summer syndrome, he continues. "Families go across the board on this. Sometimes tension goes up when they go back to school. With others, it is the other way around. And in some families it's just not an issue. In a well-organized family you don't have people trying to motivate each other. There is an automatic assuming of responsibility. You lay out your plans for the summer."

Dead silence, before the reporter (and parent of two) asks, "Just how realistic is that?"

"Pretty unrealistic." Kerr chuckles. "But you must admit, it looks good on paper."

When there are summer problems, Kerr says, a major reason is that "parents feel responsible for getting the kid going in the summer. During the school year that responsibility is relieved by school." Camp

For the middle class, paying to ship children to all those places with the funny Indian names is one summer solution. It is a solution that pleases pediatricians because they get rich - excuse me, richer - off of it. One recent morning in a Northwest Washington pediatric factory, camp-bound children were getting pricked in the arm for TB tests by the score. "It goes on clear through July," sighed one nurse. Near her, a mother said tersely to her toddler, "This is not a gym, darling." The child had just somersaulted into two kids and the legs of another mother, obviously not entranced. "Why?" asked the child. A thinner answer still: "Because this is not a gym." She stopped for one minute. Everyone stared.

There are, of course, all sorts of camp horror stories. One family shipped their son off to Eleuthra to a sailing school and it went bankrupt. They lost their money and the boy came home three weeks early. Another set of parents plunked down for two camps. Both children got chicken pox. There is no refund for chicken pox. And then there was the harried mother who sent her children off with their iron-on name tags safety-pinned on. And another who got a frantic letter the day before her daughter was supposed to return from camp several states away asking not for money, but for an entire new trunk. "I and five cabin mates used mine to stand on and, gee, how I know it was so fragile?" At Home

The man could barely talk as he thought of his teen-age son, the carpenter's helper, who did nothing but sit around the house during his off hours. "They're like . . . huge glands!" They are too old for camp and too young for a real live job.

"I never thought I'd find myself praying for summer school," said one mother, "but it's nice to know their mornings are occupied with something constructive - even if it is remedial reading."

Another mother has been nudging her ll-year-old into more summer reading and was pleased when the child said what the mother thought was the following sentence: "Oh, mom, I just read an article on Greece." The mother replied, "Oh, that's terrific dear, I'm glad you're taking an interest in ancient history." The daughter: "Oh, it's not so ancient. It's about the time you were young. The '50s. Can I go see it? Travolta can't sing worth anything, but all the kids are going. . . "

Summer duty charts are stuck all over refrigerators these days. One woman is teaching self reliance - all the children must wash and iron their own clothes. "If you don't have anything clean to wear and you have to go out, that's just too bad" was her edict. "The only trouble is, the first time that happened we had tickets to the Kennedy Center. I had also made this big thing of us doing things together as a family - so there we were, walking 10 paces ahead of these kids in smelly old blue jeans, trying to act as if we had never even met them, let alone belong to them." Grandparents

Another sweet solution is to ship the children to grandma and grandpa, although some of them are getting up pity and think they have a place in this "me-first" era.

One grandmother, now having the time of her life as a high-powered executive in the Carter administration, said of summer visitations: "We're laying very low on that one. We're made about this little girl. As long as we can visit her. Which we did. Once."

Another grandmother who lives in Palm Desert, Calif. - where the temperature reaches 115 in the shade - tells her daughter with sweet innocence, "Oh it's much too hot out here for the little ones in the summer, dear."

And nowhere, in this survey, could a victim of the empty-nest blues be found.

Which reminds one of the mother who purportedly occupied a home in Chevy Chase. One by one she saw her children leave the nest. As the last of five left, her husband waited for their first summer of silence, fearing a possible nervous breakdown on his wife's part.

As he turned the key in the door one balmy summer's eve he was greeted by his wife walking down the staircase. She wore nothing but a champagne glass in her left hand, and this salutation on her lips: "Alone at last." To Work Or Not to Work

One woman in counseling said her main problem was keeping her children active. She was checking the newspaper ads, hounding the children. "The kids weren't terribly mobilized: they had a pretty nice summer staked out. . . not doing anything." The woman's solution? She went out and got a job herself.

For the psychiatric social worker who barely survived June, there was a different solution. She quit. "There is this double guilt. I'm leaving all these problems of poor, mainly single-parent families - women who cannot not work.We're an elite and our problems are zero, compared to what chaotic and deprived families go through. Many of these mothers must work unbelievable jobs, cleaning jobs in offices that go until 3 a.m for example. They rely on what free summer programs are available and their kids, like one said, "You know, when I get bored, I get into trouble.'"

To work or not to work is a common dilemma and there isn't a working mother who hasn't envied a non-working mother and vice versa at some point come summer.

One working mother who used to make it to the office on time now slinks in late, already exhausted from a full day of buying name tags to put in the shorts that had to go in the trunk that was just dragged down from the attic only to remember, at the last minute, that it had a hole in the bottom from last summer which has to be taped. Now she's going to have to sneak out to lunch early because if she doesn't get the trunk off by costly express service her kid will be the only streaker at camp.

One male parent and husband of a working wife said, "We barely make the system work all year - I walk them to school. Her job is over in time to pick them up at 3 p.m. But now one is in a camp in a neighborhood park and the other is taking sailing lessons - 10 miles away - both start at the same time. And one gets out before my wife gets off work." The solution is for her to leave work a bit early and for him, the driver of the would-be sailor, to arrive late for his job.

They are all holding on for that ultimate in family togetherness: two weeks vacation in August, "if we live that long."

The non-working or part-time working mother views summer from another angle.

There is absolutely no acceptable excuse for them not to car pool the tennis team or swimming team, they complain.

"I'd give my soul to work full time," says one mother of four, amid familiar clicks of children picking up the extension phone. "My husband never understands why you're so tired after a day hanging around a community pool. You have a terrible headache and everyone's lost his or her bathing suit, and you've spent the day brushing up your strokes because the teen-age lifeguard - a simply adorable child of your best friend - is spending the whole time talking to her boyfriend while your little one is heading for that spot just under the diving board. And why is it that I am sitting here worrying about the 3-year-old from across the street who somehow managed to elude the babysitter and is now three-fourths up my trellis while her mother is, you guessed it, at work?" CAPTION: Illustration, no caption, by Modell; Copyright (c) 1978, The New Yorker Magazine, Inc.