Dulles is closest at about 23 miles to the hotels (airport code IAD). Reagan is about 40 miles to the hotels (airport code DCA)
We love your kids- we really do!- but we are keeping the wedding/reception adults only :)
Cocktail attire would be just fine. Unless you have a super fab dress or suit/tux you want an excuse to wear, then by all means!
No shuttles will be provided but Uber/Lyft shouldn't be a problem to request. Its about 3.5 miles (about 10 min drive) from the hotel to the wedding venue.