Yes, it seems unnatural to me that you would wake a sleeping child so they can just eat. If someone did that to me I'd be throwing things too.
Have a family meal in the evenings. Goodness gracious! Poor kiddo!
That said.
I understand where you're coming from, wanting that ideal that really doesn't exist except in movies.
To be truthful and completely honest I'd say this. If you and your wife sat down and decided that this is the life you want, getting kids up at 5:30am and transporting them over an hour away then when wife gets off work around 6 or 7 or later when they get home....
I'm sorry, I know there are thousands of people who do this on a daily basis just to have a good paying job and not live in DC, it's not a place you'd really want to live, but please consider the life you're giving your kids.
Wake up at 5:30 to dress and eat. Then travel an hour to go to child care until it's time for her school to start. Then she goes to school and back to child care until mom picks her up and then they start the drive home. Only to get there and eat then it's off to bed....what kind of life is that for a child?
She doesn't get to play with the kids her age in your neighborhood. She won't be making friends she can go and do anything with because everyone she comes into contact with is either a child care worker or a teacher from school then you, mom, and sibling.
I suppose you both picked this lifestyle because you want your child to go to this particular school. I can't imagine anything at all would influence me to this degree where a child would be traveling an hour each way for school.
Next year please consider that your child needs friends, she needs activities she can do, friends that live near you that she can bond with and start making lifelong friendships.
Both your children need to be going to the local elementary school and living a child's life not a commuter's life.
I do think it's okay for your family to wake up early if you want this. I know people who wake up at 6am so they can do family stuff together but they didn't do this until the kids started school. They don't go to bed at 7pm either. They go to bed around 8 or 9pm. They do activities together after mom gets home, they do swim team and do races on the weekends, they do a LOT together.
You're not the only family that faces this sort of lifestyle. I would never make a little kid get up to eat with me just because I have this desire to eat breakfast together.
Here's the situation where your lifestyle would work.
You live in DC and it takes mom 10 minutes to get to work. Everyone gets up to see mom off to work then you take kiddo to school on time. Little sibling gets in the vehicle and you take big sibling to school. Then go run errands or back home to do your daily stuff.
If you can possibly put the kids in a local, to you, school please please consider it. If the school they're going to is so wonderful that it is the most awesome school you can imagine them going to them please think about moving closer to mom's work. I can't imagine the kids traveling to and from DC like this.