J.S.
This may be a defense mechanism--if she is not finding any success in academic areas--and everything is hard for her at school (and homework at home) it may feel safer for her to be "bad" rather than be "dumb" among her peers (please don't take that wrong--I am not saying she is dumb--I am suggesting how she might be feeling)
Is she young for her grade? Does she seem less mature than her school peers? Would another year in first grade next year be beneficial to her to help her get the basics down before going to 2nd grade. I would definitely discuss the possibility with her teacher--not that you want to decide anything concretely this early in the school year, but if you and the teacher agree that this is a definite possibility/probability, it may be okay to lessen the pressure--reduce what is expected of her this go around in first grade--knowing she will grow up and mature this year and give her a chance to meet all the 1st grade expectations next year in her retention year. Just something to think about. I wouldn't think of it as a failure--at that age a lot of kids just need that extra time--first grade is just a different experience from Kindergarten or any other type of experience most kids have had--and some little bodies and minds just aren't quite ready for it.
Another possibility I wouldn't jump into, but I would definitely start exploring is if she might possibly have a learning disability or something else that is causing her difficulties in school. Just keep in close contact with her teacher and other professionals at her school (counselor, administrator, etc) and explore all possibilities. My experience (as an educator) with kids this age is that inappropriate behavior is often a symptom of other things. Very few kids that young are ever maliciously trying to misbehave.
Good luck.