What your daughter needs is to fail at something, Mama. It's better to let her fail now so she learns it by the time she is a teen.
Yes, I have totally bailed out my kids when they flubbed a school project or assignment. I've also let them screw up too. Because they knew that I would let them screw up, when I DID help them out, they appreciated it more.
If I were you, I'd send a note to the teacher, telling her what transpired. Tell her that you decided to let her teacher explain to her that she didn't go by the directions. Sometimes the teacher needs to be the "bad guy" and it's okay for you to tell her that. She will understand.
That being said, when my older son was in 4th grade, he could not seem to write his biography of someone whom he had to also give a presentation on. I had to help him write it. He was not pissy with me, I will say. He just couldn't seem to write this thing. It was a big assignment. I wrote the teacher and told her exactly how much help I gave him. She and I talked about it later - she told me that there is a school of thought that sees parents "scripting" for their kids (especially boys) for a while in school to be very helpful to them. In my son's case, she was right. I never had to script for him after 7th grade, and it was mostly for larger assignments. The last thing I did was help him shape a term paper in high school, by showing him how to move his paragraphs around so that they would flow better. He is in college now and writes lots of papers and makes very decent grades.
So, go ahead and make her do the work (like you did while she was being babysat.) But let her get a lower grade after she says she doesn't want help. When she brings a grade in and marks from the teacher about how she didn't do the assignment right, THEN tell her that next time, she should listen to her mother. Maybe she won't, but at least she will start to learn the lesson.
Btw, no, you all don't need family therapy. You just need to let her find out herself what happens when she doesn't follow the directions. And after teaching 10 years of preschool, I know you aren't being sarcastic. However, you have to remember that though kindergarten is a higher standard from preschool, you are jumping a little high by trying to help her plan through her projects. Let the teacher do that.
Good luck,
Dawn