Any box with an "I" for "Independent" in the corner is meant to be done independently (including the reading) by the child. There is a fair share of it in CTC, which is appropriate for that age, so she'd probably have enough on her plate with that - especially if you are working on the heart issue of complaining.

BTW - good for you to identify it and choose to work on it with her! We're working on cheerful attitudes here too, mainly with one of my ds's in particular, and usually in regard to the topic of chores.

So, I understand this issue well and think you are wise not to let it dictate your selection of materials.
Your dd will also be independently reading books for Drawn into the Heart of Reading, probably using Level 4/5 of the Student Book as you teach the 4/5 plans from DITHOR. Here is a link to the available book packs for that level:
http://www.heartofdakota.com/drawn-into-optional4-5.php
I think that's enough to assign for school, but if you would enjoy having her read some of the extension titles, she could do that as well. Those titles are really meant for dc aged 12 and 13 though, so I think I'd shy away from that (mature content), and let her focus on cheerfully studying CTC's core instead.

If you just want some free reading for her, you can do what I did and just look at the HOD book shop and pick titles from previous guides we didn't get to use (i.e. the Storytime books in the 2 sets we didn't use in Bigger Hearts - since you only use 1, etc.) and have those on hand for her to read at her leisure. HTH!
In Christ,
Julie