Oh, boy...have we been there! First of all, you need to have the school counselor & the principal in on the meeting too. We have gone around and around with the schools. We've had teachers tell us that it isn't their job to be "policemen"...and watch the kids do their work in class. There are some truly dedicated teachers out there, but they are getting harder and harder to find. I do know the politics involved....low pay, etc....but my thinking is that if they don't truly want to teach, then they should go get a low paying job somewhere else. We need teachers!
If Taylor needs extra help at school, then it's the school's job to get it for her. They may need to do some testing, and of course they will want to "label" her....it's a legal process for the school so that the child can qualify for the extra help. But if that's what it takes, then you need to do it.
If you don't want her labeled with a learning disability, then the least you can do is try to get her moved into a classroom where you think she and the teacher might get along better.
Find out if the teacher has a website for homework. Our elementary school had a phone number you could call, to get each teacher's homework for the day. But then, you would also need to have extra books at home...the school should be able to give you these.
There is NO legitimate reason for a 3rd grade teacher to not be able to see to it that Taylor has her assignments written down, and then initial it.
Our kids have "agendas"...a book that they are required to write their homework in and have us sign, and the teacher initial. They can help you with this....you just have to press. Make sure that you start out with a positive attitude, and only get nasty if you have to.....