Your day sounds a lot like our day.
I get up around 6 am with my husband and from 6 am-8 am is when I get any "me stuff" done. I check e-mail, organize the day, list phone calls, errands, maybe do a chore.
By 7:30 or so my son wakes up and usually plays happily on his own after a cuddle and a nurse at the computer. He usually eats a banana.
My dd doesn't get up until around 9, and we usually eat breakfast pretty much right after that.
The main "school" portion of our day is a 30-40 minute circle time, which I try to do at 10 am. But for example, tomorrow we are meeting a friend at the park at 10, so if they are up early, we'll squeeze it in, maybe a shortened version. Or we'll just skip it. We do fingerplays, songs and verses, and end with a story (same story repeated each day for a week).
After that we usually play outside until lunchtime. I might stay in the house and fold laundry or clean a bit, or I might take a book out to the hammock. Or I might sew or do handwork. Usually I end up doing nothing, hanging out in the yard while they play, or making phone calls. Next week we'll be ready to start gardening so I will dig and prepare the beds while they play and join me if they like.
We have lunch, then usually pursue something Katie's interested in. For example, we might look up the lady slipper flower online since we heard about it in the story. Today she asked me to help figure out how much her Barbie would cost at Big Lots that she has been saving up for. ($3.99 plus tax, I showed her how to calculate tax, so $4.27, we counted out the 27 cents change together, then she played with it and another dime to make different quantities and counted them to herself. Then she made a game where I had to guess how much she had if she had 2 dimes and 3 pennies, say -- she told me if I was right.

)
Around 1:30-2 we will do our project of the day -- nature walk, baking, painting, or a craft.
After that we pretty much veg out until dh comes home. Maybe play outside again, or watch a little TV, have a rest time.
The evenings go: dinner, clean up dinner, pick up toys, bath?, brush teeth, pj's, stories, sleep.
Oh, my kids are 5 1/2 and 3 1/2.
And things are totally different if we go anywhere! But I'm trying to keep to circle time right after breakfast.