If it is true that your daughter has work to catch up on, then you should have her stay to do it, but if it is done she should go as usual. And, being her mother you don't need HIM to tell you that. Ignore, and do what's right.
Stick to the schedule, and if you email anything keep it short and say you are trying to keep the schedule consistent for the kids because with the divorce there is enough change in their lives. End of story. Whenever you write you have to think how the court will take what you say because you know he will keep anything he can use. Or, go ahead and stick in how, since you were home with them for x many years, AND homeschooled them, YOU are definitely aware of what they can and cannot handle workwise and outside activitywise. He is getting info. about homeschooling to use in court. I would guess he is trying to show that you didn't school them correctly or enough and will try to use what he finds as evidence of that. ...slither...slither....