This is normal. I think they all do it. She's definately ready for potty training.
My theory about why she says "No":
What she's doing is finding ownership of her own poo poo and pee pees and this is great for potty training. You can let ther know that she can own them and put them where she wants - in the potty or in the yucky diaper (sorry, only two choices)-except for mistakes. Ya know, if no one is around, other than you, to be bothered with the smell, you can even ask her if she wants to keep her poo poo for a while and give it a poke so that she really feels it in there. And then, every 5 minutes (for about a 1/2 hour) ask her if she'd like you to take it out. I do this while I talk about how uncomfortable it is and how she/he can't sit down to play toys because the yucky poopy is in there. I make it a little uncomfortable to deal with. What that does, is it lets them learn about the feeling of poo poos in the pants and they get trained to come to you for the diaper changes rather than run away.
Does she also seek a sneaky private place to push it out? Probably so. My 15 month old just started doing that, and then running away from me when I say, "Oh, you are doing a poo poo. Let's take it out!" I do however, let her keep it in there for a little while... eventually she comes to me with an irritable whine to take it out. And my heart leaps that the tables have shifted; success! The goal is that, they learn to come to you to get cleaned up afterward. But if you keep catching it sooner and sooner in the process, like midstream, she'll start comming to you as a resource sooner and sooner to the point where she's asking to be taken to the potty before the poopy comes out.
So, that's my theory and how I work it out. It's too bad you missed the summer. That's the best time for potty training. I suggest nakedness as much as possible so those poopies can't be hidden in any way. And I don't suggest training pants or underwear because those can even give them a sense of diapered security. Also, make life all about potties and flushing. Talk, talk, talk, about it all the time. God gave women a long attention span for a reason. Nagging is just female asset applied wrongly. I encourage you to use your God given ability of consistent in this area.
Testimony: My oldest was potty trained between 15 & 18 months old. My newest girl is starting already at 15 months old. But, we missed the potty by about 5 feet today (whoops, set backs are part of the process). I set her on it, she pushed and pushed, nothing came out.... then, within a few minutes after walking away, 'plop, on the floor'. That's pretty close; she knows what's going on. And my boy -he's another story. Having gone through cancer treatment last year... he's a little behind at 3 years old. After an intense summer of getting it through to him to use the potty, when he knows better, we have been sucessfull enough to be accepted into pre-school (where you have to be potty trained). The older they get with this, the more the power struggle because they are smarter, sneakier, and they've developed more skills on how to power struggle with you.
Take care of this while she's still sweet. Hope this helps.