her cage is HER home so she would go to it...
are her wings clipped? Even a bird with clipped wings can fly "a bit". Especially if they are starting to grow in new flight feathers...do you know if she is doing this??
by persistent I suspect you mean you kind of chase her around till ..she gets on your finger...this is not establishing trust as your basically forcing her to do this.
don't tire her out by chasing her around the cage trying to train her... this is just exhausting her and leaving her no choice...she gets on your finger because now she has been basically forced to do that.
a tame bird is more than willing to jump on your "hand" and want to be with you ...also don't move her to another room to train...train her from where her cage is normally kept...just make sure you have taken time to birdie proof the room in case she quickly manages to get by your hand and gets out.
it sounds like she is also coming out of the cage so if this is true how do you return her to the cage???
also do you try to take her out of the cage or does she come out on her own???
she is fluffing up like that because she is tired and you have worn her out...also are you grabbing her at all???
females are a bit slower to learn also...are you sure its a female as generally they cant be truly sexed till about 8 months old????
and perch training should come first...its more important than training to get on your "hand" not finger...you can buy a wooden dowel at any hardware dept in a store so buy a long one...don't use one from the cage.
until you answer all these questions it will be sort of difficult to give some advice...