My DS is 2.5 and never says yes when I ask if he needs to go. Very rarely does he tell me ahead of time that he has to potty. I am starting to think that he's just not going to tell me till he's like 6 years old - seriously!! And this is why - he (like all toddlers) is so in the moment. He will dance around and hold himself, even dribble in his pants. I'll say "look at what you are doing, you are feeling like you need to pee. It's time to potty." But no, he says "I just HAVE to finish this puzzle" It's not that he wants to pee in his pants, but he can't stop playing, and he can't see the benefit of pottying now so he doesn't pee his pants in 10 minutes. The here and now is so much more important.
As for the sitting on the potty and then pooping in the pants 20 min later - I think that is an independence thing for a lot of kids. Almost like, it's my body and I will go where and when I want. Maybe the naked time and potty in the pack n play would work. Or a little potty in the bathroom and naked time from 2 till 2:30 potty time and let her choose to go sit.
Every kid is so different and what works one month may not the next.