I'd recommend Mystic Conn Seaport as well and also really close is the Submarine Museum. Now that's not Pirates but it is cool!
Mystic does have Pirate Days but may not fit your travel time:
Mystic Pirate DaysStay there a few days, then head to Salem Mass - They have a Pirate museum
Salem Pirate Museum - is small but my girls enjoyed it - was led by a tour guide that was a hoot. Here's my post from our
New England Trip when we went to the Salem Pirate Museum
Pirateland is a campground heading South - near Myrtle Beach, SC -Has a Pirate Theme and highly rated.
Though I never did this - did see a Pirate ship trip at the Jersey Shore
NJ Shore Pirates - check that out on your own....
Good Luck, and enjoy the time with your family.