My daughter just turned three and it was the same thing for the past three months - I gave her the ultimatum of when she turned 3 she had to use the potty all the time. Even three weeks ago she was still holding the poop and peeing right in front of me when she just told me she didn't need to go.
Now she is doing it "all by herself" and is pooping too.
Give her a goal - if she is a very independent child, like mine, she will need to have the satisfaction of it being on her terms (so she thinks). Once she gets that feeling that it is her responsibility to make it to the potty - I think you will have a much easier time.
Since the birthday has passed - try to choose a point in time for her to shoot for. I would talk about that certain point in time - perhaps it is somewhere fun to go - pump that event up as much as you can - show her pictures of it so she can get an understanding of it. You will need to have her parents on board with this too. Then tell her that she can go when she doesn't have any more accidents. Then let the next few weeks run the course - talk up the event, counting down the days, mark it on a calendar and make it part of your routine each day. If she has an accident - remind her that in two weeks (or whatever time) she needs to use the potty all the time. Do NOT make a big deal over the accident - if she poops/pees or whatever, say oopsy - maybe next time you can try to go on the potty. Make her go get her change of clothes and she should be able to change herself. If it is a poop accident then help her minimally - she can get herself dressed after she is cleaned up.
Also reward any and all potty - I know you have tried it - but if she is going pee pee in the potty regularly then make the poop reward HUGE - popsicle or ice cream cone. Make the poop reward a party. Then ween her off the reward. It will get easier - but do not make a big deal of the oops'.
My daughter still has an occasional pee pee accident - mostly when she is totally engages in playing with something or outside. I do make her go potty right before she goes outside, or we go somewhere. If you are in the car and she has to go potty - try to encourage her to hold it - that was part of the problem - she didn't have the holding control quite yet.
Lastly - limit the consumption - make sure she isn't chugging a juice box down all at once. Teach moderation - that helped tremendously. Encourage take a few sips at a time. I think part of the pee pee accidents was due the all of a sudden urge to potty that she just wasn't used to controlling/holding.
I hope this helps some - it worked for me - my older son was trained within a week at 30 months - then she came along and it was quite a bit longer. They all train differently and I don't think family history will give any reasons why.
Good luck!