She probably gave back the sword because it was her own fault that you became a Dragon Knight in the first place and she felt guilty about it. If she had kept you more close, nothing would have happened (but it would make for not a very exciting game).
I think she gave you the sword cause it was rightfully yours. And it was not her fault that you became a DK. She ordered you to stay behind in order to protect you, to stay safe in the village. A newly created not complete Slayer will definitely get toasted against a dragon. You disobeyed her others and Talana/Ygerna got you. She felt betrayed by that and got pissed which is understandable. And the fact that she didn't kill you herself near the Temple was cute :))) On your second meeting in Aleroth she's furry-ous (hot! xD). Well, not only did you betrayed her but you also killed her man and a true Dragon Slayer would rather sepuko than accept the dragon xD
