We took my DS (Year 3) out of school at Easter so have only been Home Educating since then. You and I sound quite similar and I won't pretend there aren't any arguments! However, there is no question that DS has made great progress in many areas and is now challenged and stimulated; he definitely doesn't want to return to school so it can't be going too wrong.
What age is your DD and how big is the class she is in? She clearly has an enquiring mind but it sounds as if the school is not particularly interested in helping her in areas that she needs support. Nobody knows your DD as you do and no-one else will care as much about finding out what works best for her: my experience of schools is that they want to be able to tick all the boxes with the minimum of effort.
I can understand your fears of not being up to the job but that may well be partly due to not having tried it before. How about doing a week's trial for a couple of hours a day to see how it would pan out for you?
At my DS's level, I'm not finding it difficult at all: in fact, I've really enjoyed researching subjects and tailor-making worksheets/problems/tasks for him. I have help from my DH here and there which is reassuring. Also, we had a visit from the LA education consultant; she was very thorough, taking time to look at the work he's done at home. She was very complimentary so that boosted my confidence. Perhaps your council would be able to put you in touch with an EC to talk things through before making a decision.
There are some excellent workbooks around which are useful as a guideline and to fall back on when you are running out of ideas. I also take the view that there are tutors around if I get really stuck although I appreciate that that may not be an option for everyone due to the cost.
Are you thinking of HE just for your DD or other DC as well? Would you have practical support?
Good luck with the decision making and enjoy the sunshine!