Women's Freedom

Isn't it historically inaccurate for Katherine to have so much freedom?

Not really. One has to keep in mind that the common sources of information on medieval women came from the writings of church fathers, theologians and preachers as well as literary works - romances, poems, moral essays and tales. These have been taken literally with no allowance made for artistic exaggeration or satiric intent.
It is worthwhile to note the book, "Memoirs of a Medieval Woman" by Louise Collis. The book is about a woman who deserted her husband and fourteen children to journey across Europe meeting famous people and getting into all kinds of trouble. Margery Kempe was a real medieval woman, strong willed and free to do as she pleased. Armed with this kind of information I thought it was well within the realm of possibility for Katherine to exercise her own freedom.