Hair is a toughy. The best I can find is to do the bare minimum, even only 2-3 minutes'-worth, while she's watching something really fascinating (in our house that has been certain videos or screen-savers, or Daddy being a lunatic).
As for nails, my ds went through an extremely unco-operative phase at about your dd's age, so we ended up taking him to sandpits as often as possible and taking his shoes and socks off, even in the winter. That kept his nails 'filed down'. We did get some strange looks, though!
After about a year of this, I suggested that he count '1, 2, 3' while I was positioning the clippers, and then shout 'ELEPHANT' and by the time he'd finished, the clipping would be finished. Again, I only ever did 2 or 3 nails at a time. The 'Elephants' has become our mantra for anything unpleasant.
He has grown out of it now, and lets me trim his nails with my manicure scissors, so it does improve!