I saw the response about public bathrooms. I just wanted to add, that I keep a potty in my mini-van. Before we go into a store, or before we go home, whatever's necessary, my daughter, and/or any of the other toddler's we're with, use it. I usually find a patch of grass or roadside weeds to dump it. I have scented trash bags from a dollar store, to throw away any toilet paper or solids, the same as I would do with a diaper. It has worked great for us !!
I also agree with going straight to underwear. You just have to be ready with lots of clothes to change into, and enforce a schedule for yourself to ask if they need to go. Pull ups are great when kids won't lay down for a diaper change anymore, but they still fell like and do the same job as a diaper. JCPenney has a great waterproof matress pad. I think they need to feel the embarrassment, discomfort and all that's involved in an accident. They need to develop through it, and learn that it's not accepted to wear diapers any longer, or have accidents. I think a bit of dissapointment from the parent is OK...but my Mom always told be to not say "shame" on you!! Just telling them it's too messy and they need to tell someone they need to go. If they're ready they will get it.