How old are your kids? April in the Carolinas can be all over the place - it is usually warm, but this winter has been unusually cold. We usually see people in the ocean in April, but they are all Northerners!
Myrtle Beach has tons to do even if it is too cold to swim - mini golf, the aquarium, Ripley's Believe it or Not,
Wonderworks (which is awesome), shopping, restaurants, etc. There are several places with indoor pools and some with indoor lazy rivers, but they are not luxury resorts. Our favorite resorts in Myrtle Beach are the Marriott Grande Dunes (which has an outdoor pool) and the Marina Inn Grande Dunes (not on the beach, but they have a shuttle to a private beach or you can drive). Resorts like Dunes Village, Landmark, Sea Mist, etc have more amenities for kids (lazy rivers, slides, some have bowling alleys), but they are just ok hotels.
We really like Hilton Head, but most of the stuff we like there is outdoors. It is much quieter than Myrtle Beach, so it depends what you are looking for.
Charleston is lovely and has lots of historical sites and great restaurants as well as nearby beaches.
Wilmington has the Battleship NC, a nice Children's Museum, one mini-golf place, Airlie Gardens, the Cape Fear Museum, the Serpentarium, river tours, and a nice riverfront area downtown. We like Wrightsville Beach for beach time, but some people prefer Carolina Beach.
Charlotte would be a lot of fun if you were looking for a city getaway. Charlotte has
Discovery Place (which is awesome for kids and adults), the
Whitewater Rafting Center (which also has rock climbing and ziplining), a Great Wolf Lodge in Concord, and the Nascar Hall of Fame (have not been there, but in case it interests you). Even if you didn't stay at Great Wolf, you could find a hotel with an indoor pool.
Hope this helps!
Edited to add:
I didn't mean to diss our capital city. Raleigh has some very nice arts and science museums, and the Carolina Hurricanes play in Raleigh. If you like hockey, the Hurricanes games are very fun! Raleigh has good shopping, too, but if coming from Maryland, you probably have all the same places and more.