I tried the summer when ds turned 3, gave up after a few weeks, left it until the next summer, he was 4, got the hang of peeing quite quickly, but he was reluctant to pee or poo, in pants or nappy, by then... but dry at night!
He was terrified of public loos as well, refused to use them, unless they didn't have a hand drier.
The summer holidays he got the hang of peeing in the potty/toilet, but poo was a nightmare, he became constipated, we had him on senna and lactulose. He didn't want to poo - nappy or toilet/potty. Slowly over 6 months we had more and more success, no accidents at nursery from the term after we started training him.. he got there, it took him longer than nt children. Christmas past he just started using the loo for both, though he still preferred the potty for poo.
This summer at the age of 5, he gave up the potty, is happy to use the loo and no problems with constipation, he still needs prompting to go to the loo, but will ask now and again. He even used a portaloo.
I don't think there is any magic bullet, that your dd probably can do it, with lots of patience, determination and being as relaxed as you possibly can (easier said than done, quite a few grey hairs appeared in the last year!) The difference between my ds when he was three and now really is amazing, he has matured so much, is much more reasonable and verbal... still has asd(not dx yet)/language disorder, but just has grown so much in every way!
When we were going through it all it was very very hard, but I really thought my ds could do it - I think as ds's main carer most of the pressure was on me to read the signs/understand what was going on with him, which was pretty tiring!
Good luck!
I think our first break through came when ds saw wall.e, he really wanted a wall.e toy, we got him one(put it on a high shelf so he could see it) and promised him he could have it if he managed to use the potty, it was a huge incentive, bribes hadn't worked before then, but this was something he really wanted! After that it was chocolate stars/buttons etc but we stopped giving rewards way before he got the hang of using the loo properly.