It sounds like things have gotten overly stressful at home, and possibly a bit boring for your daughter st school. Sherry Z is right about the negative impact parent stresses have on the children who pick up on it. There are probably a few things that can be helped once you know what to do, but there could be underlying issues that may need more attention. Just do a lot of observing what is going on so you can pick up on it if there are some issues that may need further assistance. You could write them in a journal which can help identify what may be going on, along with any impact it's having on those involved. Which could be helpful in the future. Also take some time for a few real good one on one talks with your daughter about anything that may be bothering her or anything she enjoys. It would be a very good thing to spend some quality time with her alone each day, even if for just a few minutes.
I have a daughter who is also 6, and has trouble in school because she get's distracted, doesn't pay attention, and wants to play. She is very smart and should do very well. The biggest problem she has we identified last year. She has done well with almost everything expected until Kindergarten when she had to start writing regularly. Her writing was and is very sloppy, hard to read, and doesn't go along with many of the usual handwriting rules. This may not be an issue for your daughter, but see if there is anything she's not doing so well with. With my daughter I started out trying to push her to improve, and practice with my help each day. That just increased her frustrations and mine. Her handwriting did get slightly better before the year ended, but she did far less of it because she doesn't like that she's not good at it. Anyway, toward the end of the year I talked to a friend who works in OT at another school. She suggested some ways that may ease the process, make it more fun, and help strengthen her ability to write. She also suggested that maybe I should try to pull back a bit, and not push so much, maybe it would come along. I had been thinking that myself. Haley is good at so many things but is very sensitive, and the negative attention was getting her more discouraged, to the point that she didn't want to bother. I have pulled back and been more reassuring and her writing has gotten much better.
The attention problem and wanting to play is still an issue, but I think that is normal to an extent. Once they reach 1st grade they are still expected to work on some of the same things as in Kindergarten but they have to get much better at it, they have to do far more, and they have to start working on more complex things like using money, adding and subtracting multiple digits, writing correctly, and using fractions. This may be overwhelming if some of it is difficult, but it may also be boring if some of it is being repeated over and over for practice, or if it is being worked on for long periods of time. Some kids need the extra time and practice, but some kids may do better advancing on to things that are a bit more challenging and a bit more interesting.
I am thinking that a little more structure with discipline and keeping things she isn't supposed to have away from her vision and her room, should help out. The stress that is throughout your home is going to be picked up buy the children, and is probably a big reason for some of the disobedience from your child. Yes, her problems are feeding your stress, but your stress is feeding her problems and everyone's stress. It's just creating a viscous and expanding cycle of stress, and negativity. You may want to consider making a list of your expectations along with a list of possible consequences for not meeting those expectations.(Try to keep it short, include your husband in the process, and choose your battles.) Then try to match up consequences with the expectations they seem to go well with. Pick out one consequence for each disobeyed or disrespected expectation that seems to fit well. You may want to get input from the whole family when you are deciding on possible consequences. Try to make sure it doesn't put too much concentration on negatives, actually you may want to put in some positive consequences for meeting expectations and doing good things. Once you have established a reasonable set of expectations and consequences, explain it to the family and follow it. Leave the stress and anger at the door and just follow your expectations every time. You could even post a big copy of these expectations at the front door, and have pictures next to them to represent each one. It can serve as a reminder to everyone. It can also help inform others of your expectations.
With her home work, set up a time each day when someone can sit with her if she needs encouragement or help. She may need a little time to unwind when she gets home so you could allow a play or relax time at that point. Keep the homework fairly short, and not too late or she will get too tired to do decent work. You may want to provide a five or ten minute break, just don't do it often or the work won't get done. Try offering incentives for work that is done well (at school and at home), it doesn't need to be junk, and it doesn't need to be expensive, but it should be positive and should offer some encouragement. It just sounds like things have gotten so negative that it may be outwaying the positives, and dragging your daughter down. Just remember that while encouragement, challenge and attention can be a powerful thing, discouragement and negative attention can be a very powerful thing as well.
Take another look at the post early on from Jen. It may have sounded kind of harsh, but she made several very good points. We all have tough times in our lives and some times we need to take a step back, take some deep breaths, and retool a few things that maybe are increasing stress and chaos. That can sometimes help improve things for all involved.