I understand a lot of what people are saying. But I have to disagree with some of it.
Like forcing vegetables. If I do not force DD to have fruit (and I have to blend it every morning or it doesn't get consumed) and eat her vegetables, she would just eat carbs. And she has bowel problems. It isn't an option not to force her. Not about to start giving her a laxative a day because she hates fruits and vegetables. So using this analogy... she has to be forced into healthy habits because of health concerns for her. She really has issues with the bowel.
So, staying with my devil's advocate role, how different is that for someone whose child is HG, even PG and doesn't have learning passion? What would you do, just let them slide?
And hates, really hates when we try and show her a better way.
Well...I feel that if a child doesn't appear to have a learning passion, it could just mean they haven't found it yet or they aren't fond of the methods used to teach it.
And in my humble opinion, early reading does not make or break the gifted child. However, forced learning can.
There's plenty of ways to incorporate learning into fun ways. Hands-on activities are much better for some kids. Plenty of learning going on with science experiments, nature study, playing math games, new vocabulary words and concepts are picked up through exploring math and science. You just can't read about them and get the same experience as working with experiments, or using geoboards or pattern blocks or playing other math games simply for fun.
It sounds like your dd likes to sample different things, new experiences, but when the novelty wears off, she becomes disinterested. Or, if she at all senses disappointment that she isn't sticking with something, she could be picking up subtle hints even if you are praising her efforts.
If she really hates when you try to show her a better way, it's probably because she senses you might not trust her to figure it out.
I would give her a little control over the situation (whatever that is) and not jump in to trying to show her a better way (not saying that you do, but just in case). Rather than say, "here, let me show you how"...maybe you can say, "It seems to be frustrating you. You could either keep trying, or you can ask me for help, or you can take a break for a while and try it another time".