What is the ruling on a daughter taking money from her father without his knowledge, and is she obligated to return what she took, especially since she does not remember the exact amount?

You have done well in repenting from the act. You must return to your father, through indirect means, what you predominantly believe to be the amount you took unlawfully. Then, ask him for forgiveness regarding any remaining financial obligations you owe him. It is not necessary to inform him of the truth of what you were doing. The important thing is to restore his right to him.