You're right about "during" meaning "throughout". And you're also correct in your choice of an answer.
It is "During the decades.."
From my usage of the two words (In / During), I've come to notice that I use "during" with "a noun to express 'when' something happens." In your example, "the decades following the Declaration of Independence" would be the noun / subject.
"In", on the other hand, is used when talking about events to come, or a period of time. For example, "In the coming years, I will have saved enough money to buy a door for my house," or "In 1843, I wasn't alive to really care."
Correct me if I'm wrong.
Student or Learner