Heather, two things here:
1) Do your darndest to avoid homework hassles by asking the school to not send homework. I got to the point where I only used homework as something to give difficult child 3 to do when he was home sick from school (which was most of the time, due to his anxiety). I told the school that if he was sick I wanted worksheets from them, but if he was attending school then I would not insist on him doing homework, because after him trying to hold it together all day at school, to make him do more when he got home was too difficult for him and for us all. Besides, his medications would be worn off and he wouldn't cope very well. We did our best getting him to do homework in the mornings, or if the teacher cooperated, on weekends. But NEVER late in the day, when his coping skills were gone out the window.
2) The nausea - it sounds so much like difficult child 3. He got to the stage where he was vomiting at school, often repeatedly. His teacher insisted he was making it happen, deliberately trying to retch. But I also saw him at home when this would sometimes happen (usually when we were talking about him going to school that day) and he was not trying to force himself to vomit. It is possible that at school he didn't try to stop it, because his teacher was insisting that he was NOT sick. At first I backed up the teacher and now feel like a real rat. The teacher WAS a "female dog" and is one of the worst at the school, in never listening to parents or therapists, and doing things her own, lazy way. She has since banned therapists from visiting her classroom and refused to meet with them when the parent requests it. Parents are too scared to report her for this so she gets away with it.
Back to the nausea - difficult child 3 liked school and wanted to be at school. Despite my opinion of his teacher, he actually likes all those who have been his teacher (I don't think some of them deserve this loyalty, myself). But an example - it was his birthday towards the end of the summer holidays, we were having a happy day and he asked me, "School goes back next week, doesn't it? This year, I will not let the bullies upset me. If they get nasty or hit me I will walk away and tell a teacher."
Despite that positive statement, within half an hour, he was vomiting.
This is a kid who doesn't get car-sick, he doesn't vomit at any other time. The anxiety was THAT severe.
We couldn't let the vomiting stop him doing his work, though. While the teacher would accuse him of faking it, I didn't. But I did say to him, "Honey, this nausea of yours is a problem but we know that it is NOT a symptom of something nasty; I know you have a slight fever but you actually are NOT really ill, you just feel ill because you are very anxious. If you were acutely ill, I would take you to the doctor to try to make you better. But with this, the doctor can't diagnose a bug or give you medicine because what you need is to be able to not get so upset and anxious. And we shouldn't let it interfere with your education, you just have to find a way to work with this. So you have to keep working. If you want to get in your pyjamas and go to bed that's OK, but you take your work with you and do it while you're snuggled up in bed."
That's when we brought in a rule, "School work during school hours". I did change the work around sometimes, letting him do easier work or work he enjoyed more, if he was more anxious than usual. For harder work I would let him snuggle with me while he did it, while I read my own book or did my own work on my computer. Especially when he first began correspondence school, he seemed to want to be touching me but NOT to have me help him. He just seemed to want the physical reassurance and encouragement.
What has worked best of all - to teach him to self-motivate. You're already working along that path, form what you describe. The problem is, she's getting anxious and stressed but unable to articulate the specific need properly, or to organise her thoughts. having a good vocabulary doesn't mean that she can always explain how she feels - trying to find the right label is only part of that problem. Trying to identify and explain the unexplainable is also a bit problem. She sounds like she really does want to do well and this is also adding to her anxiety.
difficult child 3 now has his work highly organised. Each subject teacher sends him his worksheets, numbered in sequence. difficult child 3 does them, I sign them to say it was his own work, date them and post them back to the school. If difficult child 3 has a question he can ask me because I generally know the answers, but too often he prefers to telephone the teacher himself. (He did this today - his maths work asked him to identify the median of a series of scores, I told him how to do it for an even number of scores, I got it up on Wikipedia, difficult child 3 chose to confirm this with his teacher. Hey, he prefers the authority. I'm cool with it.)
difficult child 3 got angry with me a few weeks ago when I said he was falling behind. He works hard but has the occasional 'off' day, and these are catching up with him. So he calculated what week of the school year we were up to, and then checked off the worksheet numbers. OK, I was right. He wasn't happy about being behind. So we worked together on a good rate of work to aim for - two worksheets a day, to keep up and catch up. He chooses which subject, out of the pile of work waiting to be done. We discuss which days would be best to do certain subjects - save the easier subjects for more stressful days, for example.
But he is motivated to do well, and I encourage. I use bribes - he wanted a comic book and I bought it for him so he wouldn't worry about the shop selling out, but I told him he could only have it when certain worksheets had been completed - about two days' work. He asks for a treat like an ice cream, I tell him he can have it when he's completed that day's worksheets; to treat himself as a reward.
I help him when he asks but he generally chooses to not ask because he feels that if I help him then it's not his work. He's had several teachers tell him that it IS still his work, that they want him to learn by doing, not be perfect immediately. If I read him a list of words and their meaning, that's OK because by typing it all down, he is learning. If he takes two days to look them up in the dictionary and then types them out, that it a waste of time.
Basically, a perfectionist kid can be very difficult with homework when they know they are not functioning at their best. The anxiety can be VERY nasty and needs to be acknowledged before you can teach her to ignore it as best as she can. She isn't faking, she isn't being a drama queen (although I do call difficult child 3 that sometimes) - she just needs it acknowledged so you can then encourage her to carry on regardless. Because illness can only be an excuse up to a point - after that, when your schoolwork begins to suffer, the reason doesn't matter once you get a failing grade. They can't pass you if you fail, just because you were sick. If you don't know the work you can't build on it the following year. If this is because you were lazy, or because you were sick - it makes no difference. You still have to do the work. Once you can help her understand this, and help her see that you want to work with her to help her reduce her anxiety, then things can turn around.
With difficult child 3 we use various tricks to reduce his anxiety - essential oil of lavender in an oil burner; a lava lamp; soothing music; a plate of fruit or sandwiches. it only works a little bit, but every bit counts.
It's a hard road, but as I said, you're already on the way.