It looks like you are working hard to ponder what will fit your situation best right now.
In looking over your scenario, there's a few things that I'll mention that may be of help to you as you ponder. The poetry in Preparing Hearts is mainly built around discussion with the parent/teacher, which makes it tough for your daughter to do independently. In looking for independence, she'd be better off doing the poetry from Beyond as an independent assignment. This would work for her, as it goes well with the history in Beyond and she is also sitting in on Beyond's history.
In removing the poetry from Preparing Hearts from your schedule, you will likely want to add a creative writing component to replace the creative writing lessons scheduled within Preparing's poetry. You may wish to do this by using Igniting Your Writing vol. I which is a once weekly independent writing course written directly to the student. The Teacher Notes are provided in the back to guide you as you check your child's work.
This would work well for this time in your life, as the creative writing lessons with in Preparing Hearts will require parental guidance.For Bible Study on Days 1 and 2, I would have your daughter go over the assignment in the Bible Study box on her own first, and then meet with you later for a brief discussion of the questions. Days 3 and 4 of the Bible Study box will be independent each week.
Science should be mostly independent, except for Day 2 which is a narration day. At this point, I would have your daughter narrate to a younger sibling rather than waiting to narrate to you. Have her give the sibling the book open to the pages upon which she is narrating. We have done this with my second and third sons, and my third little guy loves it! Science is now his favorite subject as he gets to hear all the fascinating details from big brother.
As far as Drawn into the Heart of Reading goes, if you are short on time and unable to meet with your daughter for it on her assigned day, there are emergency options in the back of her student book (for the days when there is no paper and the student is meant to meet with you to do the lesson). Utilize the Emergency Options as needed to get you through this time and keep your daughter going forward in her reading. I applaud you for getting her going with DITHR! Way to go!
One other thing to consider is that you could assign your daughter to do the read-aloud for Reading About History to all of the kiddos from Beyond. This would free you up, but would also be great for her! It would be another independent task for her too, depending on how well everyone listens. Perhaps, she could read it aloud to everyone at lunch? I find when mouths are full, minds are open! We do feed our toddler earlier than everyone else, so it's quieter at the lunch table during our read-aloud time.
Just a thought? You could also listen to the Hide Em in Your Heart CD assigned from Beyond as they're seated at the table right before they eat, and then quickly do the memory verse and the few questions from the Bible Study part of Beyond. Then, your older daughter could read the Reading About History selection and follow it up with the poetry and rhymes. You could copy the poem so everyone had a copy, or each pair of kiddos could share. Your daughter would already be familiar with the poem from her independent reading of it earlier in the day.
Then, all of the kiddos could do the rotating bottom left box in Beyond after lunch together. After that you could finish up with Storytime. If you'd done the language arts, reading, and math in the A.M. from Beyond and Preparing Hearts, then you'd be done with Beyond at that point.
Just thinking out loud.
Blessings,
Carrie