We play. We read. We go to the library. The kids go to camp in the morning for half the summer (chess, drawing, fencing, robot building) and that is enough. We may have one or two goals for the summer (my rising third grader needs to memorize his times tables this summer, learn to tie his shoes) but nothing else. If one of my kids was struggling with something we might focus on that. The summer is a time to be free.Do your kids do any studying in summer, preparing for the next grade which is not part of any assignment(s) the school has given for the next grade?
However, there are kids that are going to Math and possibly other classes for the next grade and I was like a little bit of work once a week (maybe) couldn't hurt but she absolutely is not interested in any "work" related stuff.
Not only could you end up with power struggles about going since she doesn't want to, it could make next school year worse. It's pre-teaching the curriculum, so it could make school less interesting and more repetitive.
I really think that the more choice we give our kids about their own lives the better. There are some things they can't make choices about, but when they can, I'm 100% for it. I'm also not a fan of pre-teaching material unless a child is either behind or has learning difficulty.
When my kids have done formal semi-academic classes during the summer, they were all enrichment based rather than school curriculum based. They did a thing on the legal system where they had mock trails for fairy tail characters and other stuff like that. I really wouldn't sign up my child up for the kind of program you are describing.