Dear S.,
My overall philosophy is that if something really, really isn't working and is just making everybody miserable, then the child isn't ready, regardless of that child's chronological age. Let it go, and try again in six months. I know it'll be cold, but if it's too cold to go outside, the "naked method" can actually work well.
Also, do you think your daughter might still be reacting to the birth of her baby sister? It's sometimes hard to introduce an additional new routine when a child is adjusting to a sibling, and when preschool-age children see a baby getting lots of attention, they sometimes lose interest in "big girl" things.
That said, if you really want to keep trying, I'll let you know what's sorta-kinda working with my son, who also just turned 3.
What I try hard to do is start the day with a success. My son starts every day sitting on the potty with (I hate to admit this) a video. I am normally very strict about TV, but I allow my son to watch videos (Thomas and Sesame St.) if and only if he's actually sitting on the potty. After we celebrate the morning success, I keep my son bottomless and playing *near* the potty for as long as possible. The longer we do this, the longer it's part of his consciousness. With this method, my son tells me he needs to go potty on and off through the day, but only if the potty is in his field of vision, and only if he's not 100% absorbed in another activity. The bad part, of course, is that I've become the Mom Who Lugs the Potty Around! But it really is working, and he does seem to be potty-conscious for longer and longer stretches (with some notable failures, of course).
Oh, and we haven't gotten anywhere with a sticker chart either. I've found that it works much better to reward the process (just sitting on the potty) than the product.
So ... please don't despair! Either let it go and wait until you're daughter's in a more receptive phase, or tell yourself that preschool-age children are just very routine-dependent, and it'll a lot of time and effort to introduce a new routine.
On the whining/crying thing, I wish I had the answer! My son does this too at times, and I do NOT have a magic bullet for it! The only thing I know is that on days when my son really does this, I realize later that he needed more sleep and/or food. I do feed my child and put him to bed -- really! -- but with growth spurts, etc., it's sometimes hard to keep up with fluctuating food and sleep needs, or at least it is for me. Of course, for your daughter, sibling adjustment could also be a big factor, and that just takes time.
Sorry, that was really long and rambly. But I hope it helped.
Best wishes,
Mira