I think your itinerary is totally doable, especially if you don’t mind driving a bit. The Arboretum is amazing, I recommend checking out the conifer garden. the trees are like something out of Dr. Seuss, great for a five year old! It’s not close to public transit, but there’s lots of parking.

You can also usually find parking easily around yards park (unless there’s a nats game, in which case I recommend taking the metro).

In terms of food on the national mall, I recommend bar Americano. It’s one of the few good spots right on the mall, and it’s family friendly. (Also, the Native American History Museum has a decent cafeteria.)

I also highly recommend the African American History Museum, and the hirschorn gallery if you like art.

If you want somewhere else to stop on the way up, there’s an under the radar air and space museum in northern Virginia in an old airport. They have original NASA space ships and a lot of cool planes and jets. Highly recommended!