I'm seeing this from the perspective of having older children (my twin boys are almost 16). I can't tell you the number of times I've bitten off the words "Why don't you just LISTEN to me!!??"
Example: our high school requires students to make up any days of phy ed that they miss. Now I'm not going to get into my thoughts on that; it is what it is. So at the beginning of the semester, I suggested that they do a few make-ups in advance, knowing that they would miss school for one reason or another in the next 18 week. Of course neither thought this made any sense. Sure enough, they both missed school, and were scrambling to complete their make-ups at the end of the semester. Why didn't they do it at the beginning, like I suggested? Because it was MY idea, no doubt. And my kids DO respect me, they value my opinion, and they often listen to (and incorprate) my ideas on things. But sometimes, they just have to figure things out for themselves.
As for learning better from others - I know exactly what you mean! I taught my sons how to ski, and they're pretty good at it, but they reached a point where they weren't progressing. On a ski trip to Montana, I put them in lessons. The instructor told them EXACTLY what I'd been saying for 3 years (at least it sounded the same to me), but when it came from him, they both said "Oh, that makes a lot of sense - I'll have to try that!" Their skiing improved dramatically as they practiced what he taught. While it was too bad that I had to pay for a lesson to get the point across, I was just glad that they figured it out - no matter who they learned it from.
My sons and I had the conversation just last week that we learn a lot more from our own mistakes than by being told what to do. Two years ago my DH took the boys backpacking in the Badlands of western North Dakota. It was hot and dry, and he encouraged them to drink lots and lots of water. Of course they didn't think they needed to drink as much as he said, and they both ended up somewhat dehydrated - which is very uncomfortable. Now they are both diligent about drinking a LOT of water when they're in the heat, or working hard. They will never again let themselves get dehydrated if they can help it - because they've made that mistake once, and once was enough.
My point is that your dd will learn to fold clothes or sew or swim, along with a million other things, whether she does it your way or her way. Maybe it will take longer. Maybe her results will be pretty crappy to start with, and she might be fine with that for quite a while. Eventually she'll either ask for help, or she'll live with her own results. If she pokes her finger enough with a needle, she might ask for guidance - and it will mean a lot more to her when it solves a problem that she has actually experienced.
It sounds to me like she's got a pretty good head on her shoulders. When asked what would happen if she didn't memorize a Bible verse, she understood that there wasn't much of a consequence for her inaction. In her shoes, I would be equally reluctant to invest much time and energy to the task.
Hang in there!