Tabitha,
Your post struck a chord with me, as so many kiddos struggle with exactly what you are mentioning with your own daughter. All kiddos have their weak areas, and it is sounding like your little honey's weak area is handwriting.

One thing to ponder is that Charlotte-Mason would say that neat handwriting is a habit, which needs to be worked on as all habits are, carefully and consistently one step at a time. With most kiddos who have poor handwriting, it's important to note that as the volume of writing increases, handwriting that used to be passable at best become illegible at worst.
While it is a good idea to work on handwriting in short time increments over the summer,it will be more important to address the habits she's formed with her handwriting during the school year. Likely, you should see some improvement in this area in the summer simply because it is one of the few or only subjects your child is working on, and she is probably doing very little work requiring handwriting during the rest of her day.

However, during the school year it's important to really weigh how poor the handwriting is and whether it is bordering or moving toward the illegible. If this is the case, I would begin first by cutting back the amount she is writing (meaning you would neatly write the beginning part of the assignment for her), and then she would finish the last portion neatly. Charlotte Mason would say that a little done neatly is better than volumes done carelessly. Whatever is not done neatly would need to be redone.

When they aren't writing as much, it is easier to have a child redo what is done carelessly. Then, the habit of doing written work carefully can truly be honed.
As your daughter improves in this area, she could take over more and more of the handwriting assignments herself. While this likely would feel like a backward step, it honestly is the retraining of a bad habit that has been allowed to form. I know this because I had it with my own oldest son, prior to reading more deeply about CM.

I did not go as far back as expecting perfection from him (and had I been more willing to devote more time to the retraining of this habit I should have), but I did lessen the amount he wrote and did require him to redo as needed. This helped my oldest son immensely and his quality finally improved. Honestly, continuing to write in a workbook is a crutch that will not improve written work in the day-to-day writing. Kiddos can perform it on the workbook page, and then continue their messy habits in all of their other written work. These are just my thoughts, after years of using workbooks for handwriting with my oldest son and seeing little improvement.

Diligently working on handwriting overall as a habit in all areas of written work bit by bit made the most difference at our house.
Also, if you feel that your child functions better with lines, as most children do, you can easily assign your child to write on lined paper for the notebooking assignments. Then, she can cut that portion out and glue it on her notebook page. We did this in my public school teaching days all of the time. It makes each notebooking page customizable to fit exactly what the assignment requires.
Blessings,
Carrie