Why did She...SPOILERS
In the end admit that she was a witch?
Also why did the Grandmother always hate her?
"At the end of life, we will be judged by love" ST John of the Cross
The biographers who wrote "My Only Great Passion" felt that Anne suspected having magical capabilities, and that Anne genuinely felt that she had contributed to Absalon's death. Personally, I think of it as being much deeper than that -- indeed, I personally feel that her monologue at the end relates more to a sense of personal defeat. At several points in the film, it is brought up (particularly by Herlof's Marte) that Anne was possibly forced into marriage, due to her mother being considered a witch. So once Martin's cowardice causes him to turn his back on Anne, she is not only aware of the fact that she will be burned at the stake (which generally tended to happen, regardless of the personal testimony of the accused), but that Martin's desertion has caused her to lose the only happiness that she knew.
It helps to know, of course, that the real Anne Pedersdotter was burned at the stake in (I think) 1590, several years after Absalon Pedersson's death.
As for Absalon's mother, her disposition was probably a multi-faceted issue. A lot of it stems from her dependency upon Absalon (which, one suspects, could have also been reciprocated by Absalon after losing his first wife). But she was also aware of Anne's mother being considered a witch, and felt that Anne was entirely inappropriate and unworthy of being Absalon's wife.