My grandson, going on 5, hasn't had an actual accident for awhile now, but he gets awfully close. He's so into his current activity that he just can't tear himself away until he's about to burst. This is completely normal. Sometimes we "help" him by reminding him he hasn't gone to the potty for a long time now, or noticing out loud that he's doing his potty dance. When he was younger, we reminded him more often, and made a game of going potty so that he'd be able to leave his play.
And a reluctance to go because it's a simply a bother is also completely normal, especially if the child is actually "trained" on the parents' schedule, and not because this was a natural developmental advance for the child (kids who are fully ready, physically and emotionally, generally train themselves as eagerly as they learn to walk). This isn't actually the same thing as laziness, though.
And I'm sure you know that it's a mistake to start thinking of our kids in terms of labels, because they tend to start living up (or down) to those labels. Even a glowing summary ("My child is so responsible!") can become a diffcult burden to a child. My husband grew up with that assessment from parents and teachers, and it makes it terribly hard for him to deal with any thought or impulse he may have that doesn't seem "responsible" enough.
I see from your profile that you have a somewhat older child with ADD, and wonder whether this tints your interactions with your 3yo, perhaps because you are tired and frustrated and thus excessively demanding, or perhaps because she behaves so much better than her sibling that you perhaps expect too much of her. If these, or other dynamics are her usual experience, then she quite naturally will counter them with whatever behaviors she has available to her.
This is not an accusation, this is a suggestion that you look for some dynamic YOU might be able to change, K.. Your daughter doesn't have the life experience to have a very big range of solutions to her own frustrations or needs. And every behavior can be seen as a strategy to get some need met. Kids count on grownups to help them learn better ways to deal with their emotions and their legitimate needs.
There's a wonderful parenting workshop condensed into a book that many young families I know have found to be valuable: How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. This book teaches parents how to really understand their kids' motives, as they perceive them. This is wonderful information, because then you can craft solutions that fit the child's actual needs. And the real stroke of brilliance in this book is that it teaches us how our children can help find the solutions to their own problems. We started using this approach with my grandson when he was 2.5, and it has eliminated so many problems before they had a chance to become habitual.