All kids pick battles for some control of their little world at that age; typically it's bedtime, eating, pottying,etc.
If your daughter DID do it in the past, then she knows what to do, but now that she's in the stubborn "2" phase, she's trying to control this particular situation. I've read in Parenting magazines, that it is suggested to begin potty training, regardless of signs of readiness, or whether or not they do more than just sit on it, around 16-18 months now. The idea behind this is for us to get our child USED to the potty before the stubborn 2's and 3's hit, where they will reject it, even if they may be ready.
Anyway, I'll tell you what my son's doctor told me when he was 3 and still not consistent. She said, "Throw out those pull-ups, they are just glorified diapers." So we had a little "party" so to speak. I took him out to get packages of real underwear (he chose the same tiny whities as Daddy wears), and then tossed the pull-ups. Same trip I also bought a mattress pad cover in case of accidents at night. My husband taught him to go pee standing up (since his issue was being afraid of the "big" toilets in public places). We made up a potty sticker chart to track progress, rewarded him with his favorite peanut butter cup for pooping in the potty. And lo and behold, things finally clicked in place, and he never had one accident in his bed at night, though all kids have accidents in their pants now and then. It's hard to stop playing to use the bathroom sometimes!
I would just do what you're doing for now, since you have the newborn, too. When she does go, praise, praise, praise, but don't force her. But you do need to be consistent with either pull-ups or panties. Going back and forth with diapers or training pants isn't helping. I would throw away (or hide) the diapers completely, so they aren't an option anymore. And if you haven't bought her underwear yet, maybe that will bring a little excitement about using the potty to her. A goal, so to speak. Hope this helps you a little.