HER NAME IS Olivia Milholland and she called about dinner time Saturday, her voice bubbling with energy and cheer, wanting to know how my son the soccer player is recuperating from his broken arm, and then she popped the question: Could we possibly put up one or two boys from the Coral Gables, Fla., soccer team coming her for the tournament this weekend?

Her call did not come as a complete surprise. Not quite. Some weeks ago we got a notice asking parents to house and feed visiting players, or to volunteer their time coordinating the tournament, manning the refreshment stands and helping with field maintenance. Somehow, the notice got lost in the house and I was off the hook.

Until she called. Then came a working mother's moment of truth. I know from experience that putting up visiting players can mean feeding them three meals, feeding and entertaining their parents and no end of maneuvering to get them to all of their tournament games at all of the different fields on time.

"Look," I said to Mrs. Milholland, "I really don't want to." Then, came the excuses. "I'm seven months pregnant, I've got a three-year-old and there are simply limits to what I can do right now. Besides," I said, delivering the final argument, "I work full-time."

"Cop-out," mouthed the resident soccer player who was listening to the conversation.

"Mothers who work full-time feel they don't have to do their parts," says a mother of four who works at the local elementary school and volunteers in the intermediate and high schools. "I don't believe that's a legitimate out. I see it in the schools as far as getting help is concerned. I feel they can do the telephoning at night, or find something else [that they can do]. I don't feel they have a right to say, I can't, I work.

"I'm sure there are many days when those of us who only work a few hours or not at all put in many more actual hours of working than those who go to a job. Because they can say they have a job, they don't take on anything else. Then, after dinner, that's the end of their working day, which in my situation is not the case. Ever."

The child-oriented suburbs were founded, in part, on the principle that all suburban families have nonworking mothers and all of them have station wagons that substitute for the public transportation available in the city. That, of course, has changed. The nonworking mother in the suburbs is as rare as the big gas-guzzling station wagon these days.

This is not exclusively a suburban problem. It's just worse in the suburbs. Not only do you have the problem of who is going to be the team mother and put up the visiting players, who is going to be the teacher's helper, the library aide and the field trip chaperon, but you also have the question of who is going to drive to the music and religious lessons, to ballet and gymnastics, to the swimming practices and meets, to ball-games and to the Friday and Saturday night movies and ice-skating parties.

Can the mother who has worked all week long in town be reasonably expected to dash home in commuter traffic Friday night, fix a quick dinner and then hit the road in the station wagon to take six kids to the movies? Of course not. The reasonable person might add here that the suburban father should do his part, but the suburban father also has been working all week and fighting the suburban traffic and he, like his wife, has barely had time to see his own children and probably has no desire to see other people's.

So what happens? The working mother is confronted with a last-minute request to help in some child's activity and the obvious answer is to say no, I'm not driving. I've had a tough week at work - find somebody whose mother doesn't work and get her to take you. It's an easy, convenient answer and some of the women who don't work for pay outside the house don't like it one bit.

"I find that the women I do car pool with who work nine to five are very rigid," says the mother of a 10- and 13-year-old. "I say, can you possibly leave at 4:30 from work to take the kids and they say, no, I work. I have a particular case right now with a gal I car pool with. She goes on business trips and the last time she decided she'd worked so hard, she'd take a vacation for a week. She left the kids with various neighbors with no provisions for car pooling except me. This is Hebrew school and I feel an obligation to bring the kids whether she drives the kids or not. It is an extra obligation on me."

There was the time she was the room mother and at the last minute had to recruit parents to provide cookies for a class party. "About 50 percent of the parents said no, they couldn't do it, they worked. I said, "what does working have to do with it?' I'd have to go out to the store and buy cookies, too, now. I wonder if they let that serve as a pat answer.

"At one point it was disastrous," she says."I had car pooling every single day of the week and I did most of it myself.

"I have this one friend who works four days a week. What she says is those parents who don't participate in driving, their kids just don't get in the car. I haven't gotten that tough." Further, she says, parents who work use it as an excuse not to car pool or help in weekend activities. "The excuse is that because they work, they have so much to catch up on during the weekends."

People tend to think, 'I've got it worse than anybody else,'" she says. "But I think all of us, whether we work inside the house or outside the house, most of us work very hard. American women work terribly hard. If you've decided not to work, it doesn't mean you get the burden of other people who have decided to work."

Of course, she's right. Working means it may be more difficult to find the time for car pooling and telephoning and housing of visiting children, but it doesn't mean I shouldn't do my share. And it doesn't mean that people like mrs. Milholland should get stuck doing all the car pooling, and phone calling and team mothering.

There are times, Olivia Milholland said yesterday, when she gets tired of it, too. "Working is an excuse. There are a lot of people who work and who do it and a lot of people who don't work and who don't do it . . . They're not saying no because they work. They're saying no because they don't want to. So when they say no, I don't say anything.

"The holier than thou thing is not a good thing to have in volunteer work. It burdens you up inside and it's not bothering them at all."

You win, Olivia. Send me two kids.