NOT a homeschooler, but just thought I'd throw out there that your HS day seems to start really early, 8am? did I get that right, maybe they need to ease into it.
Some kids (mine inc) don't cope with routines, I really struggled for the first few years of parenting with everyone telling me to do routines - of course we have the rituals like bath book bed etc but when I try to build my day around a schedule all hell breaks loose. How about you, as a person do you like routines, I know I don't so I guess my kids take after me.
You might find it easier to have a daily goal, and work towards that. Surely you are keeping the kids home because you offer something different to school, so do you really need to mimic the school day?
I second Puffins comment that PE is a need not a reward, get those kids running in the morning!
As for the math, is it possible to take it off the table for a little while? Sounds like you are still trying to find your voice as a teacher and that her love of math will come back once you are feeling better about the delivery
