honestly, i would just keep doing it with "telling" rather than "asking". my daughter was the same way, at 3 1/2 she will still occasionally will have an accident if playing. i think they just are so wrapped up in whatever is going on at that moment, they just do want to stop for the few minutes to go.
what helped way back was to set a timer on the stove. i told her when it went offshe had to go. quite quickly, she would hear it, and go all by herself. now, i dont use a timer, and she does go all on her own. but i still keep track and ask if she has to go if i think its been too long. she usually says no. then 5 minutes later i tell her she has to go. i think that gives her the oppurtunity to do it on her own, but also avoids accidents.
i think what you are doing is great!!! the rewards thing i think is good but make sure they are very simple. but dont make a huge deal of it. you dont want her to ever use it for attention since she knows how much it means to you, or to test you. just say im happy you went to the potty, and give her the reward. have different rewards for if she goes on her own, and special special rewards for #2.
the only thing i would suggest is getting daycare on board. many daycares i know of take the kids every () minutes. they dont ask because what kid would want to stop playing to go pee? im sure they just dont want accidents. maybe you could go to target to get those gerber training pants. they are like panties, just thicker. if she wets, they will get wet, but they absorb it enough so it doesnt drip down her leg. she will still need a change of clothes, but it wont be as bad. she just might get confused doing different things. good luck, sounds like you guys are doing great!!!