This hits all the wrong buttons in many dedicated parents. We've worked hard to choose the right books and lessons, make it interesting, make sure that it's tailored to our child's learning style...it's like someone sitting down to a huge family dinner that we've worked on for days and whining, " I don't want any! It's all gross!!"
Relax. It happens to (nearly ) all of us at one time or another, and nearly all kids seem to want to try how far they can get with it . Even otherwise well-disciplined kids will attempt to see if they can pull you off course.
Of course, sometimes the kids are actually right. The work may be too hard, too easy, too repetitive, too much of a review...it happens. That's okay, because you're learning how to tailor things as you go along. School teachers rarely hit the best methods for each individual child, so rest assured that you probably have a better batting average than most classrooms. If you suspect that an actual problem with the materials or the pace is the problem, try asking the kids what they would do. If that actually is what's wrong, they may have good ideas about how to fix it.
Most of the time, though, the problem is simply a desire to find out how far they can go. It's human nature, and whatever your philosophy on the origin of it, you'll probably agree that it can be frustrating. It can be dealt with, in most cases, without too much stress.
First, don't get upset. Don't be goaded into providing a show of temper. This can be hard because the kids are poking holes in your image of yourself as 'wonderful homeschooling parent.' Really, though, they're just seeing how far you'll give.
Second, establish a line below which you will not go. They must complete A, B and C, and then they can do whatever it is that they really want to do. In our house, a minimum amount of schoolwork must be done before TV, leisure-time computer, game systems, etc. There is no going below that standard.
However, that base line may be much lower than you might think: kids really do teach themselves constantly, and a child who is off building computers or trying out ideas he saw on 'Survivorman' or 'Mythbusters' may be able to leave off formal science for a while. Kids who read regularly on their own don't need reading assignments. Your budding author probably writes enough to qualify for taking English. Just offer to help her proofread occasionally. Try to look at their lives and then decide where they might need a bit of extra 'mind stretching', and spend your efforts there.
Third, occasionally throw in a fun activity, e.g., games, a trip, etc., when everyone has been reasonably cooperative about school. Don't do this all the time, though, or it will cease to be special.
Fourth, consider alternate timing. My fourteen year old son does his school easily when I email him his assignments each afternoon, and then check with him early the next afternoon to see what he needs help with or wants to discuss. Other kids may prefer a written list for the week that allows them to do, for instance, all their math on one day, all the science the next, etc.
Some kids will also do much better if their school is moved to afternoons rather than mornings, especially those who are in early adolescence. (Don't worry: most kids' internal clocks will switch back to something more conventional later on, especially when they find out that it's easier to find jobs that start in the mornings. Those who don't switch back will just make a bit more money working the night shift!)
Also, consider emphasizing the fact that whining is rude and unpleasant. It doesn't help any situation or build up other people. If they want to see changes, they need to learn to communicate with people in a way that gets results. Have a family meeting about the issues, complete with the child making a presentation on 'what she would do if she were teacher.' Encourage her to look at the issue from both sides of the coin, teacher and student. Help her realize that you have a moral and legal obligation to make sure that she can function in and be a useful member of society. Show her your state or national homeschooling laws so that she understands your commitment. Make sure that she knows that you are homeschooling out of love. In short, use reason to teach her better ways to deal with other people. That's a very important lesson to learn, probably more important than reducing fractions. You may wish to use your family's chosen punishment for whining, but remember that it's very important to teach the alternative behavior.
A very compliant child will sometimes rebel passively by doing work very s-l-o-w-l-y. That's okay: just let her work while you have some tea or do the laundry. No play, however, til the work is done! Make it as short as possible for a while, though, and give that child a lot of craft or science projects on the side. It will help her train her mind to finish what she starts, and give her a reward for finishing.
Don't forget to occasionally leave the books on the table and play games, go on trips, take walks, and so on. Then, be sure to remind them that this, too, is school!!