Thank you for describing your day! I too work part-time, with more hours in the late spring and summer. I know how much it helps to try to plan things in a schedule, as it keeps things running more smoothly.

Though we aren't always exactly on our schedule, we are usually within half an hour of it. You have done some good planning here, and you should definitely give it a try to see how it goes, and then make changes as needed.
One thing that I found that helped my dc when doing PHFHG and trying to learn some independence was to briefly go through the directions of the boxes they would have to do on their own. For example, for your dc's first morning work time, you could briefly (as in about 5 minutes) go through the 3 boxes or so you expect her do complete form 8:45 to 10 AM and have her "x" them off in the corner of each box of plans as she completes them (this helps dc see what portion of their daily plans they have finished, and what they have left). To help with realistic goals for this hour and fifteen minutes, here are the suggested time allotments for PHFHG, figuring long:
Left side of plans...
Reading about History: 15 minutes
Research/Geog./Timeline: 20 minutes
Independent History Box: 20-25 minutes
History Project box: 20 minutes
Storytime: 20 minutes
1 hour 40 minutes
Right side of plans...
Math: 20-30 minutes
DITHOR: 30 minutes (3 x a week); Creative Writing: 20-30 minutes (1 x a week)
Dictation: 5 minutes (3 x a week)
Grammar: 15 minutes
Bible Study: 15 minutes
Science: 20- 30 minutes
Poetry: 5 minutes
2 hours 10 minutes
So, you could probably expect her to independently complete the Independent History Box (20-25 minutes), Science (20-30 minutes), and either her History Project as she'll probably need help with this more semi-independent box (20 minutes), or have her do Bible Study as this can be more independent and you can follow up with her later easily by asking the questions and listening to her say her Bible verse (15 minutes). I think you could easily do this at the start of your 15 minutes for Reading about History and snack time on couch.

However, if the Bible Study box is getting done and going well with dh, by all means - keep that up! By taking 5 minutes to go over the History Project with her before she starts her independent block, I think she'll be more successful with completing it (I'm basing this on what my ds needed for this age

). Actually, if she is completing these 3 subject areas within an hour and 15 minutes, she is doing things exactly right!

At the tail end of your Reading about History time, I would read through the directions of the Rotating History box with her and make sure she understands it and gets off to the right start there. She should be able to finish that in about 20 minutes or so, while you read to your Beyond... dc.

I'd set the timer for her. Then when she finishes her rotating box, you could have your Beyond dc do their poetry copywork, while you read the Storytime for PHFHG to your dd. So, now she should be done with the entire left side of plans and possibly Bible Study. It's probably 11 AM then, right? You really have a fair bit of teaching let yet, for all dc. I wonder if it would be good to take your walk and do lunch here? It seems like she needs a break, and also some playtime with her siblings? You could do the walk and then have her play with siblings as you get lunch on the table? Just an idea, but not sure about piano needs, etc.. However, either way, the idea is she needs to be done with her left side of plans and possibly Bible Study by now, and she can have those boxes "x"ed off, so she can visually see her progress - very motivating.
It's maybe noon? I think you have several teaching blocks left now. For dd, this 45 minute block could work well...
all at table: dictation (5 min.) , grammar (15 min. only having her write one small section, doing rest orally or on markerboard), math (15 min. teaching part only); on couch or somewhere else: DITHOR/Writing (10 min.) doing your lesson, hearing her read 2 pages out loud to you so you can help her pronounce any difficult words), and then leave her for the last 30 minutes to finish her math and any DITHOR while you meet with Beyond group. With Beyond group, you could do your left side of teaching "Reading about History" at this point. 30 minutes should suffice as you've done Storytime already.
It's maybe 1:30 (maybe lunch took longer or piano was in there, so I'm figuring long)? Now all that is left is the right side of Beyond and for dd, poetry (5 min.) and checking DITHOR and math. Probably about 30-45 minutes. You could enlist dd in helping with Beyond group if she is done - would she like to be in a "teacher" role? Or would she like free time? After they finish, this should be around 2:15, which is pretty good!
I totally get that these exact ideas may not work, but it seems that dd may benefit from a concentrated teaching block of time with you in the afternoon, as this will move her along and keep her on track. It also seems like she may want some time with the siblings. Maybe moving the walk and lunch/playtime a bit earlier would come at a good break time for her without her needing another break again then for a bit, which helps YOU out as you can finish her school and get to your Beyond dc's school before it's getting late. I bet your dd would LOVE to finish BEFORE the Beyond... dc?!?

It's funny, but for our dc, finishing last isn't great. My oldest ds is in high school and gets up very early in the morning (in part) to finish at the same time as the others. If the above doesn't work, another idea would be to put a big play break in the middle for older dd to play with siblings for an hour, and then finish from 3:30 to 5 or so? We are doing that this year, and it is working well! Also, marking off her boxes herself will help her see her progress and how much she has left. That motivates both of my older dc immensely, and they feel more in control of their work Hope something here helps!
In Christ,
Julie