Hi L.,
my daughter, Aradia, will turn 3 in May and is just potty-trained now. She is also very smart and extremely articulate (in 2 languages!) I will just tell you what I did and you can consider whether or not you think it might work for you.
Because I had my second daughter just 15 months after the first, I couldn't bear the thought of 'training' Aradia. I just didn't have the patience for that. Instead, when she started showing a little interest we picked out a toilet for her (she got to choose between my two favorite) and then we put it in the most-used bathroom (the one the girls are always following me in to all day). The point is, it was just there for her to see and to sit on or play with the pretend flush (that claps and cheers when pressed). About 6 months ago we picked up 'The Potty Book' for girls. Aradia likes to pretend to be the main characters of all the books we read, and so I played on that with the 'big girl, Hannah' from the book. I had no intention of 'training' her, much to my mother's disappointment, but just to expose her to the idea. So, we started reading that book together quite often, with me stressing the difference between babies and big girls (i.e. big girls wear underwear and only go potty/poo poo in the toilet). Everytime she was in the bathroom with me I would explain that I was a big girl and didn't have to wear diapers because I only went potty in the toilet. Then, everytime she cried and moaned because she hated diaper changes so much, I would explain that all she had to do to stop having diaper changes was to stop peeing in her diaper and go on the toilet instead. We switched her to pull-ups, I recommend the Dora (think they're Pampers) ones, because they are less bulky than the others, feel more comfortable like underwear, but have a strip that makes the child feel wet, but keeps your carpet and furniture dry! I would also tell her that 'Aunt Jen goes potty on the toilet, Ava (closest little girl friend) goes potty, and any other person she admires goes potty only on the toilet so they don't have to have diaper changes (you may have noticed the repetition).
Finally, one day about a month ago, when Aunt Jen and some other family were coming to visit, Aradia announced that she was a big girl and was going to go on the toilet that day. So, we switched her to some underwear that Santa had brought (as gentle encouragement) and she went on the toilet all day. She was so proud. She's been going on the toilet ever since. She wears 'special magic sleepy-time underwear' (pull-ups) during naps and night. I explained that sometimes when we're sleeping we don't always know that we are going potty, so to keep her bed dry and her stuffed animal friends clean we wear these special magic underwear.
I think with most toddlers, especially the very smart ones, it needs to be their own decision. I stressed to Aradia that it was her choice: if she didn't want to have diapers anymore, she just had to stop peeing or pooping in a diaper and go on the toilet instead.
I would suggest gentle encouragement, not pushing. Not only does that give your daughter control, but also releases the stress on you. It's her choice to become potty-trained, not your responsibility. When you relax about it, I bet she will too. Especially if she wants to go to dance class. (Instead of saying "you have to go potty on the toilet to go to dance," say "all those big girls in dance class only go potty on the toilet". That way you're just making an observation, as opposed to telling her what to do.
Sorry for the book! Hope it helps a bit.
:) T.