Both Uses of

acknowledge
in
Gone with the Wind

As always when she heard the truth spoken, no matter how unpalatable it was, basic honesty forced her to acknowledge it as truth.†
Chpt 4.39 *

acknowledge = recognize

But, if she did not smile, people would think it strange and Scarlett hated to acknowledge, even to herself, that she was jealous of a little girl, especially when that little girl was her favorite child.†
Chpt 5.58

Definitions:

(1) (acknowledge as in: acknowledge her or the truth)
express recognition or appreciation of someone or something; or admit something
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Specialized senses include sending an "acknowledgement" (letter or other message) to indicate that something was received and the "acknowledgements" section at the beginning of a book where an author recognizes and thanks other people who helped in creating the book or ideas contained in it.