Most kids find that when they don’t do stuff, their folks get into a tizzy, yell at them a little, and then bend over backwards to make things all better so that they’re not perceived by teachers and other parents as bad parents. This encourages micromanaging or “helicopter parenting”. Except for a little temporary yelling or nagging, there’s no real consequence or learning opportunity for the kid, because the parents have made it their problem.
I found the best thing to do is to back off. Don’t make it your problem. Talk with the teacher, explain your new parenting strategy, and let your daughter be tardy and take the hit. If her grades can take the hit, then perhaps the teacher needs to find a consequence with real teeth, like making her stay after class the same number of minutes helping out, or staying in that long at recess time to “pay back the class” for the minutes she stole in the morning. But the bottom line is that her school performance isn’t about you.
This isn’t to say she’s totally on her own. But she needs to come up with a solution to her tardiness. And remember, it’s always fair game to say, “Dad, I don’t know how to solve this, will you help me?” THEN you can suggest charts and stickers and alarm clocks and whatnot, and she can try what she thinks will work. But until she’s accepted that this is her problem, and she’s got the power to fix it, you’re not going to win. It’s going to keep being your problem, and she’ll just keep assuming that you’re going to clean up her mess - literally and figuratively.
Teeth brushing, IME, is just a never ending nag fest. It’s gotta be done, no one wants to do it, and you’ve got to tell the kid explicitly, twice a day, “go brush your teeth now.” My son is 15. I’ll let you know when he starts brushing his teeth on his own. PERHAPS, at 9, a toothbrush or toothpaste that she picks out will make it more appealing, but probably not for long. We did have a bit of success requiring him to pay for his own fillings (a result, the dentist testified, of his not brushing well or frequently enough), but ideally you want to prevent needing those fillings in the first place.
For the dishes and household chores issue, I found rewording things to be helpful. Sounds silly, but, “We’ll watch television after your room is clean,” goes over better than “You may not watch television until you clean your room!” The first is positive and empowering - it says what you CAN do, the second focuses on what you CAN’T do. It’s stifling, and authoritarian. Think about how you feel at work when your boss says, “If we meet our sales goals for the third quarter, I’ll pop for a pizza party!” vs. “There will be no more company sponsored events until sales goals are met.” The first makes you think, “OK, cool, we can do that!” The second makes you think, “Fuck you.”
For these and other parenting theories and techniques that I stole, check out the books in the Parenting With Love and Logic series.