That sounds tough. I do not have much experience with a strong-willed child so my advice is probably not any good.
Why do you feel you need to keep the momentum going during the summer? DD is starting kindergarten next fall and I am so looking forward to this summer for all her lazy days and relaxation. And, DD is currently in a play-based preschool part-time. So, it is not like she needs the break. I am not a homeschooler. But, that does not mean I am not fostering learning at home. I keep a calm house free of TV and video games and full of books and creative play. And, I am always surprised by how creative DD can get during a boring day--That's why I love summer.
One boring morning she discovered that dominoes had math problems on them. (adding up the lines.) One boring morning she used bananagrams to write our sentences. The best part? She thought to use upside down Js for question marks. One boring morning a strip of paper became a ruler to measure things which she then converted to cuisenaire units. One boring morning she just up and decided to read a book that was two levels too high for her before I woke up--She would have never done that had I asked.
I know my DD is bright. She is years advanced in reading and math. If she is happy, I don't worry about academic things. I think of that as an advantage of being ahead. I do worry about keeping that love of learning alive.
Yes, she is a beast that needs to be fed, so to speak. But, I also want to keep her hungry for more.
