Here's a really helpful site that gives some great "readiness" checklists, plus the skinny on the various approaches to potty-training, their advantages and challenges. It's fantastic that you've got a daughter who's willing to sit on the potty and has some success with it. But based on what you describe, I wonder whether she is ready for success yet. See if you can find your situation here: http://www.parentingscience.com/toilet-training-readiness...
Potty training is ultimately a process that the child must control, or else she's not trained. A number of factors are needed for potty training to succeed: the child must be able to notice and recognize the urge before it happens, she must have adequate sphincter control and the ability to hold it long enough to get to the potty, she must understand the point of training, and she must want to be trained. She must connect with the body sensations that indicate complete voiding. It sounds like at least one or two of these is still missing for your sweetie.
It's helpful to know that night training is a whole separate step for many children, and can lag a year (or several) behind day training – although some kids stay dry all night even before they're day trained. But for many children, their sleep is too heavy for the full-bladder signal to get through, and/or the sphincter isn't strong enough to hold a full bladder. They really are not doing this on purpose, and many of them are horrified and ashamed of not being able to stay dry through the night.
Poop training is often a whole separate step for some kids, too. A few succeed earlier with pooping in the potty. Many figure it out later. It's a whole different set of sensations, generally more effortful, and some kids equate it with losing a piece of their bodies, which can be frightening.
Sometimes rewards work in the short run if only motivation is lacking. But that introduces the very real possibility that rewards/bribes will need to escalate to keep him motivated, and that is a mistake that you will seriously regret someday.
So, what I would suggest is that, as hard as this will be, you drop your expectations about "training." Tell your daughter you are proud of how well she's growing up, and express your confidence that she will use the potty when she's ready. And she will (it sounds like your daughter is getting close to ready). If they haven't become discouraged by weeks or months of failure, kids WANT to make this developmental step when they're able, just as they want to walk and talk when they're able. Your daughter will probably need some "space" to work it through for herself – to focus on her sensations, on cause and effect, and not on mommy's eagerness or possible rewards. Or she may need a few more weeks or months.
Almost all of the kids I've known who trained the fastest, often in a day or a few days, simply arrived at that point themselves, and when they expressed interest, their parents acted as "assistants" or "facilitators" rather than "teachers" or "trainers." There's a wide range of ages when this can happen, but it's usually somewhere between 24 and 40 months (usually on the earlier end of the spectrum for girls).
Meanwhile, you can continue to make all your messages about using the bathroom as positive as possible. That can include modeling how easy/quick it is for you or Daddy, reading potty books or watching potty videos, having his toys/stuffed animals role-play pottying, and in general making a game of it. With my grandson, once he could do it but didn't want to take the time, I would go into the bathroom and begin noisily ejecting all the dinosaurs that were crowding the room and sitting all over the toilet seat. My grandson couldn't resist that game, and would come in and help me wrestle the beasts, and claim his spot on the toilet.
