I'm not sure you are powerless tbh and there is still a whole term of y2 to get her into better habits before she hits KS2.
What about asking for an appointment with class teacher when she has a bit more time. Explaining that you would like to help dd with her concentration and focus, and does she have any suggestions.
One suggestion would be, you check at the end of each week with dd's teacher how she has been. If she has been focused etc (mainly) she gets tokens towards some kind of highly desired treat. If not focused, she doesn't get to watch tv on a Friday after school. ( Or some such arrangement).
If there is work that the teacher thinks she should have finished or done more carefully, perhaps you could take it home over the weekend for her to complete/re-do. It will probably only take a couple of times of doing this for her to realise it would be better to do it properly in the first place!
If may be that just knowing you are on to her will be enough for her to sharpen her act a bit.
It might also be worth talking to your dd about what concentration and focus really mean. She is still quite young and may not be so aware of how she is working (or not working as the case may be). Perhaps you could have some "practise" sessions where she does some work with you at home and you can point out when she is pratting around going to the loo and taking ages to sharpen a pencil and suddenly deciding she needs an urgent conversation with you/the cat not so focused and when she is, so that she gets to feel what "focused" is like. You could set a timer for 10 minutes and see if she can stay concentrating hard for that length of time. What about a challenge chart where you start seeing if she can concentrate for 5 minutes, then 6 etc and mark how long she can manage on a bar chart? If you can get her to feel proud of managing to concentrate that will probably help a lot.
If she is getting all level 3's, is it possible that the work is a bit too easy for her so she is coasting a bit because of lack of challenge/boredom? One to ask her teacher maybe?
I'm sure school will be addressing it with her, but a double-pronged approach with home and school supporting each other always works best.