Your 8 year old doesn't sound like she's lazy or unfocused; she sounds like an average 8 year old. For young children, play is the work of life. Now she needs to add school work to that list of things that are her work.
Most kids don't have a natural sense of self-discipline; it's hard work and not very rewarding. Kids have to acquire self-discipline with parental help. That's part of your job as a parent.
Right now, though, this is stressing you both out, so here are some ways you can both get back on track.
Don't fight or nag over schoolwork.
Just don't. It's frustrating for you, and empowers her to divert your energy in a manner that gets her out of doing homework. Kids can cast all kinds of bait out there (it's normal). Don't take it. If you need to have discussions about respect, feelings, desires, frustrations, etc. - and everyone should get to express these things in a loving and trusting relationship - do it sometime other than when homework is supposed to be getting done.
Set up a specific time for homework.
Figure out a time that suits your child and you/your family, write it out and post it on the refrigerator. Then stick with it. Maybe after a brief relax and snack after school/before dinner/after dinner, with a bathroom break before it starts (just not before bedtime).
Let her know that there is a time to eat, a time to do homework and also that there is free time. Ten minutes of homework per grade level is the recommended norm, so at grade 3, she should have no more than ~30 minutes a day. That's reasonable and doable (hopefully for both of you).
On no homework weekdays, consider keeping that time for quiet time where she can read books or do other non-technology learning things.
Sit with her while she does her homework.
Most young children require a parent's help getting started, and need help staying focused too. It's perfectly OK. Also, sometimes fussing starts because a child is not confident about the work and feels anxious. In this case, do her homework with her to see if she understands how to do it, or feels particularly stressed over some aspect of it.
Even if she isn't, at first spend the whole time sitting there. After learning what her assignment is, work out the first problem or two (or listen to her read the first few sentences) to make sure she understands the work at the level that's expected. Then read a book. (This also reinforces that reading is important both as a child and as an adult.) Studies have shown that the best students are the ones whose parents spend the time involved with their schoolwork. As she learns to do her work, you might be able to leave her alone for longer periods (this earns her rewards, too!)
Have a predetermined, clear, reasonable list of rewards and consequences.
This can be discussed and negotiated with your child at a different time, even over ice cream! But be specific. When she finishes her homework, she gets to do things she likes to do. A video game, a TV show, read her a story, time outside, having a friend over, etc. Work on this with her.
A sticker chart for bigger rewards is good, too. A week of doing her homework without fussing/within the allotted time/whatever is most important to you should earn her 'big girl rewards': a long board game she loves on the weekend, an outing to the park/swimming pool/movies/bowling/a cookie-baking session, etc. Four weeks without fussing/etc.? A sleepover for her friends with pizza, ice cream and a movie is nice (something special for her), a trip to the beach, a shopping day, etc. Let her learn that good things happen as a result of complaint-free homework.
Consequences for not doing homework: she doesn't get to do any of those things until her it is finished. If she holds out all evening (her choice up to a point; don't argue), the next day, she gets to try again. Don’t take away privileges for more than a day. If you do, she'll have no incentive to do better the next day.
What if she starts fussing? Don't engage. Use a timer for homework, and stop the timer if she starts complaining (unless she's asking for help with something). If it goes on too long, a short time out (no toys or other activities) might be in order. Start it again when she returns to her homework. No sticker for that homework session.
Praise all effort.
Praise effort - holding back from complaining, sitting quietly, working on solving problems, etc., rather than criticize lack of effort or bad attitude. Sincere praise for things she's able to control - trying, sitting quietly, not complaining, getting it done on time, etc. - is very helpful and empowering for children.
Try challenging her from time to time.
See how long it takes her to get her homework done on average. If you see her dawdling, you might offer her a reward for extra effort form time to time, e.g. for every minute that she gets it done earlier than 30 minutes, she might get, say, an extra minute or two of computer time, story time, or even to stay up an extra few minutes. Sometime, as she's getting better at doing her work on time, you see if she wants to try to beat her best score. Keep it light, though, and pressure free, and make sure her answers are correct!
Sorry this is so long. I do wish you good fortune in working with your daughter to teach her responsibility, and the rewards of doing well in school.
