YAY!! that is a huge achivement! congrats on getting this far, ive just recently gotten over this problem with ds2, who is 3.5 yrs old.
the thing with the undies, as he told me, is he felt like a nappy was on, untill he weed and suddenly remembered it wasnt one, at home id let him get arround without pants so he HAD no choice but to go the toilet, when he got the hang of wearing jocks, i would constantly stop at toilets when we went out, and tell him to go, even if he just tried and only got a few drops out, we did have accidents, mostly waiting for the bus, i started using pull ups, and reminding him, they are jocks, but if he has a accident, they will catch it. its been a month since we stoped needing "nappy jocks" as he called them, and have been accident free while were out aswell as at home, i still sneak one on him when he is asleep, as its easioer then changing sheets!
As for accidents when at the shops, let someone know as they have mops and all that, most of them understand if you tell them, and get it mopped up quickly, id have a spare pair of undies, and a plastic bag for the wet ones, just so she will learn they are ment to stay dry!
good luck.