Baltimore/Washington International Airport and The Philadelphia International Airport are equivalent distances from Rehoboth Beach (about 2 hours).
We recommend renting a car - both international airports above offer car rentals, outside of that we recommend Turo; the car rental service that allows you to rent specialized vehicles and can sometimes be cheaper than a Hertz or Enterprise.
For hotel or rental home childcare, we recommend arranging through Sitter Solutions www.sittersolutionsdelaware.com