Since I live very close to D.C., I hope that I can be of help.

When you go into the museums and any of the buildings on the Mall, they will make you walk through a metal detector and search through your bags. Some buildings have the X-ray machines. You need to plan accordingly, basically like you're getting on a plane. No sharps or pepper spray (unless you want to take a chance, but I wouldn't recommend it in that part of town).

Always carry water and snacks (especially if you'll be bringing kids with you). Since you'll be doing a lot of walking, you'll probably get hungry and thirsty often. Your backpack will really help with that, and you'll save money from the expensive local vendors.

Small bills and coins are really helpful for the Metro.

I hope you enjoy it here! The Kite Festival is pretty soon, I don't know if you'll be here for that, but it's loads of fun. And the new Mammals hall in the Natural History Museum is great.