There is a direct flight from IAD to Panama City in the Republic of Panama operated by COPA airlines but it is just under 5 hours. If you stay at the new Trump hotel there you can take a ferry one of the days to an island. There are fabulous restaurants, shopping, casinos, and great nightlife.
The JW Marriott in Rio Hato is a 90-minute drive from the A/P and is a fabulous resort, but I don't think there is a casino.
http://www.marriott.com/hotels/travel/ptyjw-jw-marriott-panama-golf-and-beach-resort/
There is a resort closer to the city at the Intercontinental Playa Bonita but it doesn't have a casino either.
Good luck.