Hi, abbynellie –
Yes, you can use the DR Kit with your reluctant/hesitant reader too. As you mentioned, start farther back in the book. You might start her at the Aesop’s fable.
And providing variety by having her read aloud from the Pathway Readers will be a nice addition. You could alternate days, if you want to: doing a DR lesson one day, reading from the Pathways Reader the next day, etc.
You don’t need the workbooks. Just have her practice reading aloud. The readers have the new words for each chapter listed in the back of the books. If you want to, you might scan those lists ahead of time and see if there are any words you want to review so she will feel more confident when she encounters them in the sentences. Or just let her dive in and figure them out with a mixture of context and the phonics she knows — whichever method would work best for her personality.
Your goal at this point is to increase her fluency and confidence.